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Events of 1791
- January 25 – The British Parliament passes the Constitutional Act of 1791, splitting the old province of Quebec into Upper and Lower Canada.
- March 2 – Long-distance communication speeds up with the unveiling of a semaphore machine in Paris.
- March 4 – Vermont is admitted as the 14th U.S. state.
- April 21 – The first of forty boundary stones delineating the borders of the new District of Columbia is laid at Jones Point Light, in Alexandria, Virginia.
- May 3 – The Sejm of the Polish–Lithuanian Commonwealth proclaims the Constitution of May 3, 1791, the first modern codified constitution in Europe.
- June 20 – The French Royal Family is captured when they try to flee in disguise.
- July 8 – Composer Joseph Haydn awarded an honorary doctorate of music at Oxford University.
- July 14 – The Priestley Riots break out in Birmingham, England.
- July 17 – The Champ de Mars Massacre occurs during the French Revolution.
- August 4 – The Treaty of Sistova is signed, ending the Ottoman-Habsburg wars.
- August 6 – The Brandenburg Gate in Berlin is finished.
- August 26 – John Fitch is granted a patent for the steamboat in the United States.
- August 22 – A slave rebellion breaks out in the French colony of Saint-Domingue.
- September 25 – Mission Santa Cruz is founded by Father Fermín Francisco de Lasuén, becoming the 12th mission in the California mission chain.
- September 28 – Louis XVI of France accepts the final version of the completed constitution.
- September 30 – Wolfgang Amadeus Mozart's singspiel Die Zauberflöte (Magic Flute) premieres in the Freihaustheater in Vienna.
- October – The Legislative Assembly (France) convens.
- October 9 – Mission Nuestra Señora de la Soledad is founded by Father Fermín Francisco de Lasuén, becoming the 13th mission in the California mission chain.
- December 4 – The first issue of The Observer, the world's first Sunday newspaper, is published.
- December 5 – Austrian composer Wolfgang Amadeus Mozart dies.
- December 15 – Ratification by the states of the first ten amendments to the United States Constitution is completed, creating the United States Bill of Rights. Two additional amendments remain pending, and one of these is finally ratified in 1992, becoming the Twenty-seventh Amendment.