Centuries: 17th century - 18th century - 19th century
- January 3 - The Treaty of Tripoli (a peace treaty between the United States and Tripoli) is signed at Algiers
- February 14 - The Battle of Cape St. Vincent (1797), part of the Wars of the French Revolution.
- February 26 - The Bank of England issues the first one pound note.
- March 4 - John Adams succeeds George Washington as the President of the United States of America.
- May 12 - First Coalition: Napoleon I of France conquers Venice ending the 1070 years of independence of city.
- October 21 - In Boston Harbor, the 44-gun United States Navy frigate USS Constitution is launched to fight Barbary pirates off the coast of Tripoli (in 1805 the Tripoli peace treaty was signed on Constitution's deck).
- 1797 in literature:
- Harriet and Sophia Lee write The Canterbury Tales from 1797 to 1805.
- 1797 in music
- January 31 - Franz Schubert,Austrian pianist, composer
- February 15 -Henry Engelhard Steinway - German-American piano manufacturer
- March 22 - Wilhelm I, King of Prussia and German Emperor (+ 1888)
- March 27 - Alfred de Vigny, author
- May 18 - Frederick Augustus II of Saxony, (+ 1854)
- July 20 - Sir Paul Edmund Strzelecki, Polish explorer and geologist
- August 30 - Mary Wollstonecroft (later Mary Shelley}
- November 14 - Sir Charles Lyell, British geologist.
- December 13 - Heinrich Heine, poet