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1731 (MDCCXXXI) was a common year starting on Monday of the Gregorian calendar and a common year starting on Friday of the Julian calendar, the 1731st year of the Common Era (CE) and Anno Domini (AD) designations, the 731st year of the 2nd millennium, the 31st year of the 18th century, and the 2nd year of the 1730s decade. As of the start of 1731, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 25 – A fire in Brussels at the Coudenberg Palace, at the time the home of the ruling Austrian Duchess of Brabant, destroys the building, including the state records stored therein.
- March 16 – The Treaty of Vienna is signed between the Holy Roman Empire, Great Britain, the Dutch Republic and Spain.
- April 1 – Battle of Dabhoi in India is fought between Sarsenapati Trimbakrao Dabhade and Bajirao Peshwa.
- April 2 – The town of Raynham, Massachusetts in Bristol County is entered as a new town by the governor and court of Massachusetts, New England, America.
- April 28 – A fire at White's Chocolate House, near St. James's Palace, destroys the historic club and the paintings therein, but is kept from spreading by the fast response of firemen.
- April – British trader Robert Jenkins has his ear cut off by Spanish coast guards in Cuba, casus belli for the War of Jenkins' Ear in 1739.
- June 4 – The English market town of Blandford Forum is destroyed by fire, with the exception of 26 houses. About one-third of the uninsured losses are paid for by the collection of disaster relief money. 
- January 27 – Bartolomeo Cristofori, Italian maker of musical instruments (b. 1655)
- February 10 – George Carpenter, 1st Baron Carpenter, British Army general (b. 1657)
- February 15 – Mary of Jesus de León y Delgado, Spanish Dominican lay sister and mystic (b. 1643)
- February 22 – Frederik Ruysch, Dutch physician and anatomist (b. 1638)
- March 5 – Abd al-Ghani al-Nabulsi, Sufi academic (b. 1641)
- March 6 – Johann Melchior Dinglinger, German goldsmith (b. 1664)
- March 8 – Ferdinand Brokoff, Czech sculptor (b. 1688)
- March 12 – Ernest August, Duke of Schleswig-Holstein-Sonderburg-Augustenburg (b. 1660)
- March 23 – Augustus William, Duke of Brunswick-Lüneburg (b. 1662)
- c. April 24 – Daniel Defoe, English writer (b. 1660)
- April 28
- May 1 – Johann Ludwig Bach, German composer (b. 1677)
- May 11 – Mary Astell, English feminist writer (b. 1666)
- May 17 – Samuel Bradford, English churchman, Whig politician (b. 1652)
- June 20 – Ned Ward, English writer, publican (b. 1667)
- July 18 – Sir Walter Yonge, 3rd Baronet, English politician (b. 1653)
- August 27 – Eudoxia Lopukhina, Russian Tsarina, divorced spouse of Peter the Great of Russia (b. 1669)
- December 17 – George Lockhart, Scottish writer, spy and politician (duel)
- December 20 – Chhatrasal, Maharaja of Madhya Pradesh (b. 1649)
- December 26 – Antoine Houdar de la Motte, French writer (b. 1672)
- December 29 – Brook Taylor, English mathematician (b. 1685)