Columbia University, whose full legal name is Columbia University in the City of New York, dates from 1754, when a royal charter issued under George II of Great Britain created King's College on land belonging to Trinity Church in Lower Manhattan. The original name did not outlast the American Revolution. Teaching was interrupted by the war, and the institution reopened in 1784 under the name Columbia College, passing in 1787 to a private board of trustees whose early members included Alexander Hamilton and John Jay. The designation Columbia University was adopted only in 1896, when the school moved to the Morningside Heights site it still occupies.

The university is organised into seventeen schools. These include the undergraduate Columbia College; the Fu Foundation School of Engineering and Applied Science; the Graduate School of Arts and Sciences; and professional faculties covering law, medicine, business, international affairs, architecture and social work. Columbia was the first institution in the United States to award the MD degree. Its Graduate School of Journalism is linked to the Pulitzer Prizes, which the university administers and confers annually. Four independent institutions retain formal affiliations: Barnard College, Teachers College, the Jewish Theological Seminary and Union Theological Seminary.

Columbia is a founding member of the Association of American Universities and carries out research through centres such as the Lamont-Doherty Earth Observatory, where early evidence for plate tectonics was assembled, and the Goddard Institute for Space Studies. Physicists working at the university contributed to the first nuclear fission reaction in the Americas and to the development of the laser and maser. The historic core of the campus is a group of neoclassical buildings around a raised plaza in Morningside Heights, Upper Manhattan; the medical faculties sit further north in Washington Heights, and additional facilities have been built in Manhattanville. Its New York City setting places the university near major financial, legal, media and international bodies, including the United Nations.