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was a common year starting on Tuesday of the Gregorian calendar and a common year starting on Saturday of the Julian calendar, the 1737th year of the Common Era (CE) and Anno Domini (AD) designations, the 737th year of the 2nd millennium, the 37th year of the 18th century, and the 8th year of the 1730s decade. As of the start of 1737, the Gregorian calendar was
11 days ahead of the Julian calendar, which remained in localized use until 1923.
- July – Austria enters the Russo-Turkish War.
- September 1 – The oldest existing English language newspaper in the world, The News Letter, is founded in Belfast, Ireland.
- September 20 – Runner Edward Marshall completes his journey in the Walking Purchase, forcing the cession of 1,200,000 acres (4,900 km2) of Lenape-Delaware tribal land to the Pennsylvania Colony.
- October – The first national stage in Sweden opens, when the play Den svenska sprätthöken is performed in the native language, by the first native actors, on the stage of Bollhuset in Stockholm.
- October 7 – A tropical cyclone strikes Bengal, India, killing approximately 300,000.
- October 16 – An earthquake with an estimated magnitude of 9.3 occurs off the shore of Russia's Kamchatka Peninsula. Tsunamis up to 60 metres (200 ft) high follow in the Pacific ocean.
- November 4 – The Teatro di San Carlo, the oldest working opera house in Europe, is inaugurated in Naples, Italy.
- January 29 – Thomas Paine, British-born American patriot and pamphleteer (d. 1809)
- March 23 – Arthur St. Clair, American soldier and politician (d. 1818)
- April 27 – Edward Gibbon, English historian and politician (d. 1794)
- May 2 – William Petty, 2nd Earl of Shelburne, Prime Minister of the United Kingdom (d. 1805)
- June 20 – Tokugawa Ieharu, Japanese shogun (d. 1786)
- August 5 – Johann Friedrich Struensee, Danish royal physician (d. 1772)
- August 14 – Charles Hutton, English mathematician (d. 1823)
- August 29 – John Hunter, second governor of New South Wales (d. 1821)
- September 9 – Luigi Galvani, Italian physician and physicist (d. 1798)
- September 14 – Michael Haydn, Austrian composer (d. 1806)
- September 15 – Miklós Küzmics, Hungarian Slovenes writer, Catholic priest (d. 1804)
- September 19 – Charles Carroll of Carrollton, only Roman Catholic signer of the American Declaration of Independence (d. 1832)
- December 26 – Prince Josias of Coburg, Austrian general (d. 1815)
- date unknown – Frances Abington, English actress (d. 1815)
- January 24 – William Wake, Archbishop of Canterbury (b. 1657)
- January 29 – George Hamilton, 1st Earl of Orkney, British soldier (b. 1666)
- February 14 – Charles Talbot, 1st Baron Talbot of Hensol, Lord Chancellor of Great Britain (b. 1685)
- March 12 – Charles Alexander, Duke of Württemberg, regent of the Kingdom of Serbia (1720-1733) (b. 1684)
- March 16 – Benjamin Wadsworth, American President of Harvard University (b. 1670)
- May 3 – James Johnston (Secretary of State), diplomat, Secretary of State for Scotland (b. 1655)
- May 4
- May 10 – Emperor Nakamikado of Japan (b. 1702)
- May 17 – Claude Buffier, French philosopher and historian (b. 1661)
- June 6 – Pierre Joseph Garidel, French botanist (b. 1658)
- July 26 – Henri-Pons de Thiard de Bissy, French Catholic priest, bishop and cardinal (b. 1657)
- July 9 – Gian Gastone de' Medici, Grand Duke of Tuscany (b. 1671)
- July 26 – Johan Cronman, Swedish general (b. 1662)
- July 27 – Maria Maddalena Martinengo, Italian nun (b. 1687)
- September 27 – John Sidney, 6th Earl of Leicester, English privy councillor (b. 1680)
- October 12 – François Catrou, French historian and Jesuit priest (b. 1659)
- October 26 – Rinaldo d'Este, Duke of Modena (b. 1655)
- November 11 – Claude de Visdelou, French missionary (b. 1656)
- November 20 – Caroline of Ansbach, queen of George II of Great Britain (b. 1683)
- December 11 – John Strype, English historian and biographer (b. 1643)
- The Annual Catalogue – List of History, Divinity, Law, Poetry, Plays, Novels, Painting, Architecture, and all other Sciences books published in London in 1737