January
Michael Alexander takes office, as the first appointee to the Anglican-German Bishopric in Jerusalem.
American medical student William E. Clarke of Berkshire Medical College becomes the first person to administer an inhaled anesthetic, to facilitate a surgical procedure (dental extraction).
January 6–13 – First Anglo-Afghan War – Massacre of Elphinstone's army (Battle of Gandamak): British East India Company troops are destroyed by Afghan forces on the road from Kabul to Jalalabad, Afghanistan, by Akbar Khan, son of Dost Mohammad Khan.
January 8 – Delft University of Technology is established by William II of the Netherlands, as a 'Royal Academy for the education of civilian engineers'.
January 23 – Antarctic explorer James Clark Ross, charting the eastern side of James Ross Island, reaches a Farthest South of 78°09'30"S.
February 1 – Willamette University is established in Salem, Oregon.
February 7 – Battle of Debre Tabor: Ras Ali Alula, Regent of the Emperor of Ethiopia, defeats warlord Wube Haile Maryam of Semien.
March – Commonwealth v. Hunt: The Massachusetts Supreme Court makes strikes and unions legal in the United States.
March 2 – Gaylad, ridden by Tom Olliver, wins the Grand National at Aintree Racecourse in England.
March 5 – Mexican troops led by Ráfael Vásquez invade Texas, briefly occupy San Antonio, and then head back to the Rio Grande. This is the first such invasion since the Texas Revolution.
March 9 – Giuseppe Verdi's third opera Nabucco premieres at La Scala in Milan; its success establishes Verdi as one of Italy's foremost operatic composers.
March 17 – The Female Relief Society of Nauvoo, forerunner to the philanthropic and educational women's organization of the Church of Jesus Christ of Latter-day Saints (LDS Church) is formally organized.
March 28 – The Vienna Philharmonic Orchestra, founded by Otto Nicolai, performs its first concert.
March 30 – American physician and pharmacist Crawford Long administers an inhaled anesthetic (diethyl ether) to facilitate a surgical procedure (removal of a neck tumor).