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 Qianlong Emperor 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.
February 14 – At Lakkireddipalle in southeastern India, the new Nizam of Hyderabad, Subhadar Muzaffar Jang, leads an invasion of cavalry against the small kingdom of Kurnool and is confronted by its monarch, the Nawab Bahaudur Khan. The Subhadar and the Nawab order their soldiers to stand down and then engage in hand-to-hand combat, during which the Nawab "thrust[s] a spear into the Subhadar's brain" before he is "himself hacked to pieces." 
April 19 – the Qianlong Emperor of China visits the southern capital of Nanjing for the first time, bringing with him 3,000 staff and 6,690 horses and stays for four days 
April 20 – A month after the death of his father, 12-year old Prince George William Frederick is formally invested as the new Prince of Wales Nine years later, Prince George becomes King George III upon the death of his grandfather, King George II.
April 29 – The sport of cricket is first played in the American colonies, as a team of New Yorkers plays against a team of Englishmen and defeats them, 167 to 80, in a match in Greenwich Village 
June 14 – The colony of South Carolina reverses a 10-year old law that had imposed a tax of 100 pounds sterling on the purchase of imported African slaves, and reduces the tax to £10. The move effectively restores the slave trade to the colony.
November 17 – Future United States President George Washington becomes seriously ill with smallpox while he and his older brother Lawrence are visiting the island of Barbados during an epidemic  Washington, 19 years old, survives the virus but is bedridden for almost a month.
November 17 – The Pima Revolt begins in the area that now includes the Mexican state of Sonora and the U.S. state of Arizona, as Pima Indian leader Luis Oacpicagigua carries out the massacre of 18 Spanish settlers at Oacpicagigua's home in Sáric. The rebellion, which takes the lives of more than 100 Spaniards, is ended on March 18 after Governor Diego Ortiz Parilla permits the rebels to surrender for imprisonment.
November 29 – The Cherokee nation signs a treaty with British colonial authorities at the close of the two-week Charlestown Conference in Charleston, South Carolina, with GovernorJames Glen signing an agreement with Cherokee war chiefs led by the Old Skiagunsta of Keowee, the Raven of Hiwasee, Old Caesar of Chatuga and Kittagusta of Joree.