January 7 – The University of Pennsylvania, conceived 12 years earlier by Benjamin Franklin and its other trustees to provide non-denominational higher education "to train young people for leadership in business, government and public service". rather than for the ministry, holds its first classes as "The Academy and Charitable School in the Province of Pennsylvania" in Philadelphia.
January 13 – For the first time, the American colony in Georgia has an elected legislature after having been administered by a corporate Board of Trustees since its founding in 1732. The original Georgia Assembly meets in Savannah with 16 representatives as the colony prepares to become a British colonial province. After electing Francis Harris as the Speaker of the unicameral Assembly, the delegates successfully ask the Trustees not to surrender control of Georgia to the neighboring Province of South Carolina.
January 18 – In the aftermath of the Lhasa riot of 1750, Chinese General Ban Di arrives at the capital of Tibet on behalf of the Emperor Qianlong and the seven imprisoned leaders of the rebellion are turned over to his custody by the 7th Dalai Lama, Keizang Gyatzo. General Ban Di guides the interrogation under torture of rebel leader Lobsang Trashi and, after five days orders the beheading and dismemberment of the seven rebels.
January 1 – The British Empire (except Scotland, which had changed New Year's Day to 1 January in 1600) adopts today as the first day of the year as part of adoption of the Gregorian calendar, which is completed in September: today is the first day of the New Year under the terms of last year's Calendar Act of the British Parliament.
April 6 – Spanish Governor Tomás Vélez Cachupín of Santa Fe de Nuevo México, a province that now comprises most of the American state of New Mexico, begins the first peace negotiations with the indigenous Comanche tribe after inviting tribal representatives to his home in Taos. As a sign of good faith, he unconditionally releases the four Comanche prisoners of war held at Taos. One of the released Comanches reports to his father, Chief Guanacante, about the hospitality extended to him during his imprisonment, and more meetings take place in July and in the autumn.
April 13 – The oldest property insurance company in the United States, "Philadelphia Contributionship for the Insurance of Houses from Loss by Fire", holds its organizational meeting at the courthouse in Philadelphia to elect a board of directors, largely through the efforts of Benjamin Franklin. Franklin's newspaper, The Pennsylvania Gazette, has been advertising the meeting since February 18, with a notice that "All persons inclined to subscribe to the articles of insurance of houses from fire, in or near this city, are desired to appear at the Court-house, where attendance will be given, to take in their subscriptions, every seventh day of the week, in the afternoon, until the 13th of April next, being the day appointed by the said articles for electing twelve directors and a treasurer."  The property insurance company is still in existence more than 250 years later.
April 22 – Adam Smith, appointed the year before as a professor of logic, is unanimously elected by the faculty of the University of Glasgow to be the new Professor of Moral Philosophy "on the express condition that he would content himself with the emoluments of the Logic Professorship until 10 October", in that the 1751-1752 salary budgeted for the job has already been distributed to faculty members who had substituted for the previous moral philosophy professor, Thomas Craigie; from April to October, Smith's remuneration for teaching moral philosophy is limited to fees paid directly to him by his students (a half guinea per semester for the public class, and a guinea per semester for the private class. Smith's lectures on ethics are first published in 1759 in his work The Theory of Moral Sentiments.
June – Benjamin Franklin reportedly carries out his famous kite experiment, duplicating experiments that show that lightning and electricity are the same. According to Franklin, lightning strikes the kite that he is flying during a thunderstorm and produces sparks identical to what he has previously generated artificially in a Leyden jar. However, the report of his experiment is not made until October 19, in Franklin's newspaper, The Pennsylvania Gazette, leading 20th century researchers to doubt that he conducted the experiment, if at all, until sometime after September 28, when he had written in the Gazette about other such experiments, and that he was making a claim that he had conceived the experiment independently.
July 30 – The first of the Kronstadt canals, conceived by Peter the Great and designed to link two of the harbors of the Russian city, is completed and opened to maritime traffic.
August 3 – Edward Cornwallis, the British Governor of Nova Scotia, is recalled to Britain after being unsuccessful in pressuring Nova Scotia's Acadian population to take an oath of allegiance to the Crown or to face expulsion. His replacement, Peregrine Hopson, is more lenient with the Acadians but is reassigned less than two years later.
August 25 – The first group of the United Brethren church, commonly called the Moravians, leaves Bethlehem, Pennsylvania on a mission to find 100,000 acres (40,000 ha) of land on which to build "Villages of the Lord" for German emigres to settle upon in America; after a 450 miles (720 km) journey, they arrive in Edenton, North Carolina on September 10 and eventually purchase the
Wachovia tract, a set of lands in the western North Carolina colony.
September 2 of Julian calendar (Wednesday) (September 13 "New Style") – Great Britain and the British Empire use the Julian calendar for the last time and adopt the Gregorian calendar, making the next day Thursday, September 14 in the English-speaking world. A newspaper at the time notes the next day that "Altho' we have more than once, for the Information of our Readers, publish'd some Accounts of the Alteration of the Style, which took Place this Day, agreeable to a late Act of Parliament, in all his Majesty's Dominions in Europe, Asia, Africa and America" and notes that "The Supputation of the Year began on the first Day of January last, and for the future the first Day of that Month will be stiled the first Day of every Year in all Accounts whatsoever, which Supputation or Reckoning never took Place before this Year in any Courts of Law until the 25th Day of March", and adds, "This Day, had not this Act passed, would have been the 3rd of September, but is now reckoned the 14th, eleven nominal Days being omitted." 
October 19 — In his Philadelphia newspaper, the Pennsylvania Gazette, Benjamin Franklin first describes the performance, in Philadelphia of the kite experiment that he had proposed in his 1750 book. Although the original account makes no claim that he was the first to do the experiment (which had been done by other scientists (including Thomas-François Dalibard in May), nor that he conducted the test, and it does not give a date for the experiment, it becomes embellished as the story that Franklin "discovered electricity"; in 1766, the story first circulates that Franklin flew the kite in June, 1752, without specifying a date (as Franklin had done in other scientific accounts). 
November 3 – A hurricane destroys the Spanish settlement on Florida's Santa Rosa Island, leaving only two buildings standing; the remaining residents decide to move from the barrier island on the Gulf of Mexico and to start a settlement on the nearby mainland and construct the Presidio San Miguel de Panzacola, which later forms the nucleus of the city of Pensacola, Florida.
January 29 – After a month's absence, Elizabeth Canning returns to her mother's home in London and claims that she was abducted; the following criminal trial causes an uproar.
February 17 – The concept of electrical telegraphy is first published in the form of a letter to Scots' Magazine from a writer who identifies himself only as "C.M.". Titled "An Expeditious Method of Conveying Intelligence", C.M. suggests that static electricity (generated by 1753 from "frictional machines") could send electric signals across wires to a receiver. Rather than the dot and dash system later used by Samuel F.B. Morse, C.M. proposes that "a set of wires equal in number to the letters of the alphabet, be extended horizontally between two given places" and that on the receiving side, "Let a ball be suspended from every wire" and that a paper with a letter on it be underneath each wire. 
August 21 – After receiving a series of warnings about incursions into land claimed by the Crown Colony of Virginia (from the colony's Lieutenant Governor, Robert Dinwiddie), the cabinet of British Prime Minister Henry Pelham votes to send a warning to Britain's colonial governors "to prevent, by Force, These and any such attempts" to encroach on their lands "that may be made by the French, or by the Indians in the French interest."  Britain's Secretary of State for the Southern Department, the Earl of Holderness, sends the circular order on August 28. 
September 18 – Britain's Board of Trade sends a directive to the colonial and provincial governors of Maryland, Massachusetts, New Hampshire, New Jersey, New York, and Pennsylvania ordering them to send delegates to a summit meeting with the Iroquois Confederacy. The message instructs the governors that King George II has ordered "a Sum of Money to be issued for Presents to the Six Nations of Indians" and ordering New York's Governor George Clinton "to hold an Interview with them for delivering these Presents, for burying the Hatchet, and for renewing the Covenant Chain with them." 
November 12 – Spain's King Fernando VI issues a set of 25 regulations and restrictions for theatrical performances, including a requirement that the directors of the acting troupes "take the greatest care that the necessary modesty is preserved" and that the actors should be reminded that chastity requires that "indecent and provocative" dances should be avoided 
November 25 – The Russian Academy of Sciences announces a competition among chemists and physicists to provide "the best explanation of the true causes of electricity including their theory", with a deadline of June 1, 1755 (on the Julian calendar used in Russia, June 12 on the Gregorian calendar used in Western Europe and the New World).
December 11 – Major George Washington and British guide Christopher Gist arrive at Fort Le Boeuf (near modern-day Waterford, Pennsylvania and the city of Erie), a French fortress built in territory claimed by the British Crown Colony of Virginia. Washington presents the fort's commander, French Army Captain Jacques Legardeur de Saint-Pierre, a message from Virginia's Lieutenant Governor Dinwiddie advising that "The lands upon the Ohio River are so notoriously known to be the property of the Crown of Great Britain that it is a matter of equal concern and surprise... to hear that a body of French fortresses and making settlements upon that river, within His Majesty's dominions," adding that "It becomes my duty to require your peaceable departure." Captain Legardeur provides a reply for Washington to take to Dinwiddie, declaring that the rights of France's King Louis XV to the land "are incontestable", and refuses to back down, leading to beginning of the French and Indian War in 1754.
February 25 – Guatemalan Sergeant Major Melchor de Mencos y Varón departs the city of Santiago de los Caballeros de Guatemala with an infantry battalion to fight British pirates that are reportedly disembarking on the coasts of Petén (modern-day Belize), and sacking the nearby towns.
July 10 – The Albany Plan of Union is given official approval by the delegates from New York, Pennsylvania, Maryland, Rhode Island, New Hampshire and Massachusetts, with Connecticut opposing. The plan approved at the meeting in Albany, New York is based on Benjamin Franklin's suggestions of "a general union of the British colonies on the continent" for a common defense policy. As amended at the assembly, the proposed union calls for the British Parliament to approve the arrangement, which would encompass all of the British North American colonies except for Georgia and Nova Scotia. The plan, to be considered by the individual colonies for ratification, provides for an inter-colonial legislature (the Grand Council) composed of between two and seven representatives for each colony, depending on population. It also provides for a "President General" who can veto Grand Council legislation, a common defense budget with colonies contributing proportionately to their representation, and an inter-colonial army whose officers would be selected by the Grand Council. 
August 19 – Lieutenant Colonel George Washington is forced to confront his first mutiny as 25 members of his Virginia militia refuse to obey orders from their officers. Washington, who is attending church services at the time, quickly suppresses the rebellion and the mutineers are imprisoned before more join. 
September 2 – A powerful earthquake strikes Constantinople shortly after 9 o'clock in the evening. A Scottish physician, Dr. Mordach Mackenzie, reports in a letter that the tremor damaged or destroyed numerous buildings and comments, "Some say there were 2000 people destroyed by this calamity, in the town and suburbs; some 900; and others reduce them to 60, who, by what I have seen, are nearer the truth." 
October 24 – China's EmperorQianlong reverses a longstanding policy that barred Chinese subjects from ever returning to China if they remained out of the country for more than three years. 
October 31 – What will become Columbia University is chartered as "a College in the Province of New York... in the City of New York in America... named King's College", with the charter submitted by New York's colonial governor, James De Lancey.
November 28 – Denmark establishes the Renteskirverkontor, an office within the Chamber of Finance, to oversee the colonial affairs of the Danish West Indies (Dansk Vestindien). Peder Mariager, who had been a minor official of the Danish West Indies Company, becomes the first administrator. The colony, consisting of the islands of Saint Thomas, Saint John and Saint Croix later is purchased by the United States from Denmark and is now the U.S. Virgin Islands .
December 26 – Massachusetts becomes the third colony (after Pennsylvania and Connecticut) to reject the Albany Plan for an inter-colonial union, voting 48 to 31 to postpone consideration of the union question indefinitely. 
March 22 – Britain's House of Commons votes in favor of £1,000,000 of appropriations to expand the British Army and Royal Navy operations in North America. 
March 26 – General Edward Braddock and 1,600 British sailors and soldiers arrive at Alexandria, Virginia on transport ships that have sailed up the Potomac River. Braddock, sent to take command of the British forces against the French in North America, commandeers taverns and private homes to feed and house the troops. 
May 3 – France dispatches 3,600 troops to protect its Canadian colonies in Quebec from a British invasion, dispatching 2,400 to Quebec city and 1,200 to Louisbourg in Nova Scotia, unaware that a squadron of 11 fully armed warships from Britain's Royal Navy had sailed toward Canada on April 27. 
May 19 – General Braddock hosts Iroquois leaders Scaroyady, Kaghswaghtaniunt, and Silver Heels at Fort Cumberland, the British Army base in the colony of Maryland. The three chiefs pledge their alliance with the British during in advance of Braddock's expedition into the Ohio Country. 
At the entrance of the Saint Lawrence River, a squadron of Royal Navy ships, under the command of British Admiral Edward Boscawen, intercepts the nine French ships dispatched to save Canada; seven of the nine ships are concealed by fog and are able to reach their destination; another of the transports escapes.
July 25 – The decision to deport the Acadians is made, during meetings of the Nova Scotia Council meeting in Halifax. From September 1755-June 1763, the vast majority of Acadians are deported to one of the following British Colonies in America: Massachusetts, Connecticut, New York, Pennsylvania, Maryland, Virginia, North Carolina, South Carolina and Georgia. Contrary to popular belief, no Acadians are sent to Louisiana. Those sent to Virginia are refused and then sent on to Liverpool, Bristol, Southampton and Penryn in England. In 1758 the Fortress of Louisbourg falls, and all of the civilian population of Isle Royal (Cape Breton Island) and Isle St. Jean (Prince Edward Island) are repatriated to France. Among them were several thousand Acadians, who had escaped the deportation by fleeing into those areas. Very few Acadians successfully escape the deportation, and do so only by fleeing into some of the northern sections of present day New Brunswick. The event inspires Longfellow to write the epic poem Evangeline.
September 16 – Sir Charles Hanbury-Williams, the new British Minister to Russia, secures an alliance signed by Empress Catherine the Great. The Russian Empire agrees to provide up to 55,000 troops to defend the Electorate of Hanover against invasion by Prussia. At the time, King George II of Great Britain is also the ruler of the German duchy; the Russian troops are provided in return for an annual payment of £600,000. 
October 17 – The Mount Katla volcano erupts in Iceland, and continues ejecting ash for the next 120 days, finally ceasing on February 13. An estimated 1.5 cubic kilometers (1.5 billion cubic meters or 53 billion cubic feet) of tephra is discharged by the volcano.
November 1 – More than 40,000 people are killed by the 8.5 magnitude 1755 Lisbon earthquake. The tremor begins at 9:40 in the morning local time off of the Atlantic coast of Portugal and sends a tsunami that strikes the coasts of Portugal, Spain and Morocco.
February 10 – The massacre of the Guaraní rebels in the Jesuit reduction of Caaibaté takes place in Brazil after their leader, Noicola Neenguiru, defies an ultimatum to surrender by 2:00 in the afternoon.  Three days earlier, on February 7, Neenguiru's predecessor Sepé Tiaraju had been killed in a brief skirmish. As two o'clock arrives, a combined force of Spanish and Portuguese troops makes an assault on the first of the Seven Towns established as Jesuit missions. Defending their town with cannons made out of bamboo, the Guaraní suffer 1,511 dead, compared to three Spaniards and two Portuguese killed in battle. 
February 14 – The Maratha Navy that has controlled the western coast of India for the Maratha Empire for more than a century, is destroyed in the Battle of Vijaydurg by British attackers fighting for the East India Company. On orders of Royal Navy Admiral Charles Watson, the Royal Navy captures a Maratha ship (the former British warship HMS Restoration), sets it on fire, and then floats the burning vessel into the Vijaydurg Port where most of Maratha Admiral Tulaji Angre's ships are anchored. The fire soon spreads to the other ships, destroying one large warship armed with 74 cannon, eight gurabs of 200 tonnes apiece, and sixty galbat ships. 
September 2 – Abu l-Hasan Ali I, Bey of Tunis is forcibly removed after 23 years as the ruler of the North African emirate by his cousins, who are avenging the overthrow and execution of their father, Husayn in 1735. Hasan Ali surrenders to the rebels and is imprisoned in Algiers, then executed on September 22 on orders of the new Bey of Tunis, Muhammad I ar-Rashid.
December 14 – The play Douglas is performed for the first time in Edinburgh, with overwhelming success, in spite of the opposition of the local church presbytery, who summon Alexander Carlyle to answer for having attended its representation. However, it fails in its early promise to set up a new Scottish dramatic tradition.
February 2 – At Versailles in France, representatives of the Russian Empire and the Austrian Empire enter into an alliance against Prussia, with each nation pledging 80,000 troops.  Other clauses to the treaty, not disclosed to the public, commit Austria to pay Russia one million rubles per year during the war to pay for the expenses of 24,000 of the Russian troops, and two million rubles upon the conquest of Silesia (a Prussian province that had been seized from Austria in 1746). 
February 5 – The Nawab of Bengal, Siraj ud-Daulah, leads an attempt to retake Calcutta from the British. With just 1,900 soldiers and sailors, but superior cannon power, General Robert Clive forces the Nawab's much larger force into a retreat. The British sustain 194 casualties, but the Bengalis suffer 1,300. 
February 9 – The Nawab and General Clive sign the Treaty of Alinagar, with Bengal compensating the British East India Company for its losses and pledging respect for British control of India. 
March 14 – British Royal Navy Admiral John Byng is executed by a firing squad after his court martial conviction for failing to save British troops who had been besieged by a numerically superior French force at the Battle of Minorca.  General Edward Cornwallis, the ranking British Army officer at the battle, is exonerated of charges of dereliction of duty, but his career is ruined. Byng's execution is the origin of the phrase "In this country, it is wise to kill an admiral from time to time to encourage the others", coined by Voltaire in his novel Candide.
March 21 – Sweden signs an alliance treaty with France and Austria in the multinational effort to remove King Frederick the Great, even though Queen Consort Ulrika of Sweden is Frederick's sister. Sweden agrees to contribute 25,000 troops to the French and Austrian force. 
April 6 – William Pitt is dismissed from the government King George II to depart from the British government after several military reverses in Britain's fight against France in America. After a public outcry, Pitt is called back to conduct Britain's foreign and military affairs and given greater control. 
In the wake of public unrest in France, the King's Council issues a decree that bars anyone from writing, printing anything that would tend toward emouvoir les esprits (stir up popular sentiment) against the government, with violations punishable by death. 
April 29 – Inside a house at Stratford-upon-Avon in England, a bricklayer, identified only as "Mosely", discovers the testament of John Shakespeare, father of William Shakespeare, more than 150 years after the elder's death. The finding, done while Mosely is re-tiling the roof of what is now called Shakespeare's Birthplace, starts "what remains one of the most controversial topics in Shakespeare studies" because of disagreements over its authenticity. 
May 1 – France and Austria sign a second treaty of alliance at Versailles, committing France to sending an additional 105,000 troops to the war against Prussia, and to pay expenses to Austria at the rate of 12 million florins annually. 
June 25 – The 1755 rebellion against the Chinese Empire by Mongolian Oirat Prince Amursana is met by a Chinese army of 10,000 attackers against Amursana's 2,500 man force at their capital at Bor Tal. The rebels are able to hold out for 17 days before being routed. 
September 13 – A column of troops from Sweden begins the surprise invasion of Prussia, setting up a pontoon bridge across the Peene River that marks the boundary between Swedish Pomerania and northern Prussia. After crossing at Loitz in the early morning hours, the troops march 10 kilometres (6.2 mi) and begin the occupation of the undefended Prussian town of Demmin. Hours later, another Swedish infantry regiment charges across the border into the Prussian town of Anklam, where the city gate had been left open. 
October 14 – Of the 442 men, women and children who are convicted for their roles in the Oporto riot in February, 13 men and one woman are hanged; afterward, their bodies are then quartered and the severed limbs are publicly displayed on spikes. Another 49 men and 10 women are exiled at Portuguese colonies in Africa and India, and the others are either flogged, imprisoned or pressed into service rowing galley ships. 
October 24 – 1757 Hajj caravan raid: Led by Bedouin warriors of the Beni Sakhr tribe conducts a massive assault against a caravan of thousands of Muslim travelers who are on their way back to Damascus after the Hajj, the pilgrimage to Mecca. The attack, made at Hallat Ammar after the group has been resupplied at Tabuk, leads to the annihilation of 20,000 of the pilgrims. Those who are not killed outright die later in the desert from thirst and starvation.  According to one Arabic source, the largest attack takes place on 10 Safar 1171 A.H. (October 24, 1757)
February 22 – A fleet of 158 British Royal Navy warships, under the command of Admiral Edward Boscawen, departs from Plymouth toward North America in an effort to conquer the French Canadian territories of New France. Many of the sailors die of nutritional deficiencies along the way, including the scurvy that kills 26 of the crew of HMS Pembroke, captained by future world explorer James Cook on his first long voyage. 
February 23 – Jonathan Edwards, the famed English theologian who had assumed the presidency of what is now Princeton University only a week earlier, sets an example for students and faculty by publicly receiving an inoculation against smallpox.  Unfortunately, the vaccine contains live smallpox; Edwards develops the disease and dies on March 22 at the age of 54.
Marquis Gabriel de Lernay, a French officer captured during the Seven Years' War, establishes a military lodge in Berlin, with the help of Baron de Printzen, master of The Three Globes Lodge at Berlin, and Philipp Samuel Rosa, a disgraced former pastor.
June 15 – The first vascular surgery in history is performed by a Dr. Hallowell (whose first name has been lost to history) at Newcastle upon Tyne, who uses suture repair rather than a tying off with a ligature to repair an aneurysm on a patient's brachial artery. The case is reported in 1761 by Dr. Richard Lambert in the paper "A new technique of treating an aneurysm", published in the journal Medical Observations and Inquiries.  The new procedure of reconstructing a damaged artery replaces the practice of ligation that had risked the amputation of a limb or organ failure. 
June 26 – After the fleet finishes navigation of the St. Lawrence and arriving Île d'Orléans, British troops go ashore at France's North American territory and begin the siege of Quebec City
Madame du Coudray publishes Abrégé de l'art des accouchements (The Art of Obstetrics), and the French government authorizes her to carry her instruction "throughout the realm" and promises financial support.Molly Aster