|Covid-19|January 23 – The Civil Code of 1734 is passed in Sweden.
January 26 – Stanislaus I of Poland abdicates his throne.
February 12 – Francis I, Holy Roman Emperor marries Maria Theresa of Austria, ruler of the Habsburg Empire.
April – The Genbun era begins in Japan. The era of Kyōhō Reforms ends.
March 8 – Nader Shah, founder of the Afsharid dynasty, is crowned Shah of Iran.
April 14 – The Porteous Riots erupt in Edinburgh after the execution of smuggler Andrew Wilson, when town guard Captain John Porteous orders his men to fire at the crowd. Porteous is arrested later.
May 8 – Frederick, Prince of Wales, marries Princess Augusta of Saxe-Gotha.
May 26 – Battle of Ackia: British and Chickasaw Native Americans defeat French troops.
June 8 – Leonhard Euler writes to James Stirling describing the Euler–Maclaurin formula, providing a connection between integrals and calculus.
June 19 – French Academy of Sciences expedition led by Pierre Louis Maupertuis, with Anders Celsius, begins work on measuring a meridian arc in Meänmaa of Finland.
July – Russo-Turkish War (1735–39): Russian forces under Peter Lacy storm the Ottoman fortress of Azov.
September 7 – An Edinburgh crowd drags John Porteous out of his cell in Tolbooth Prison and lynches him.
December 7 – Benjamin Franklin builds the first volunteer fire company in Philadelphia.
December 26 - Andrew Michael Ramsay gave an oration in which he related the heritage and internationalism of Freemasonry to that of the Crusades.
Neustrelitz becomes the capital of Mecklenburg-Strelitz.
Bushehr is founded in Persia.
The Belgrade Fortress is completed.
George Hamilton, 1st Earl of Orkney, becomes the first Field Marshal of Great Britain.
A fire in the Russian city of Saint Petersburg burns 2000 houses.
Fifty-three houses in the English town of Stony Stratford are consumed by fire.
One of the earliest records of use of a bathing machine is made at Scarborough in England.
Charles Marie de La Condamine, with François Fresneau Gataudière, makes the first scientific observations of rubber, in Ecuador.
Leonhard Euler produces the first published proof of Fermat's "little theorem".
Sir Isaac Newton's Method of Fluxions (1671), describing his method of differential calculus, is first published (posthumously) and Thomas Bayes publishes a defense of its logical foundations (anonymously).
Muhammad ibn Abd al-Wahhab writes the Kitab at-tawhidt, marking the beginning of Wahhabism.
The Haidamakas raid the shtetl of Pavoloch, killing 35.
January 7 – Andrew Adams, American judge (d. 1797)
January 19 – James Watt, Scottish inventor (d. 1819)
January 25 – Joseph-Louis Lagrange, Italian-born mathematician (d. 1813)
February 3 – Johann Georg Albrechtsberger, Austrian musician (d. 1809)
February 29 – Ann Lee, English-born American religious leader (d. 1784)
May 8 – Caterina Dolfin, Italian (Venetian) poet (d. 1793)
May 10 – George Steevens, English literary critic (d. 1800)
May 29 – Patrick Henry, American patriot (d. 1799)
June 3 – Sir John Acton, 6th Baronet, Prime Minister of Naples (d. 1811)
June 7 – Fermín Lasuén, Spanish missionary (d. 1803)
June 14 – Charles-Augustin de Coulomb, French physicist (d. 1806)
June 21 – Enoch Poor, American general (d. 1780)
June 25 – John Horne Tooke, English politician and philologist (d. 1812)
July – Juan Bautista de Anza, Governor of the Spanish Province of New Mexico (d. 1788)
July 6 – Daniel Morgan, American pioneer, Congressman from Virginia, and general (d. 1802)
August 9 – Louis Joseph, Prince of Condé (d. 1818)
August 15 – Alexander Runciman, Scottish painter (d. 1785)
August 26 – Jean-Baptiste L. Romé de l'Isle, French geologist (d. 1790)
September 15 – Jean Sylvain Bailly, French astronomer (d. 1793)
September 16 – Carter Braxton, signer of the American Declaration of Independence (d. 1797)
October 27 – James Macpherson, Scottish poet (d. 1796)
Robert Jephson, Irish dramatist (d. 1803)
Li Ching-Yuen, Chinese herbalist, martial artist and tactical advisor (d.1933) (claimed)
Pierre le Pelley I, Seigneur of Sark (d. 1778)
Claudius Smith, American revolutionary (d. 1779)
Sir James Tylney-Long, 7th Baronet, English politician (d. 1794)
January 17 – Matthäus Daniel Pöppelmann, German architect (b. 1662)
January 31 – Filippo Juvarra, Italian architect (b. 1678)
February 7 – Stephen Gray, English dyer, astronomer, and scientist (b. 1666)
March 16 – Giovanni Battista Pergolesi, Italian composer (b. 1710)
March 25 – Nicholas Hawksmoor, British architect (b. c. 1661)
April 24 – Prince Eugene of Savoy, French-born Austrian general (b. 1663)
April 30 – Johann Albert Fabricius, German scholar and bibliographer (b. 1668)
September 16 – Daniel Gabriel Fahrenheit, German physicist and inventor (b. 1686)
December 10 – António Manoel de Vilhena, 66th Grandmaster of the Knights Hospitaller (b. 1663)
December 12 (burial) – Antonina Houbraken, Dutch draughtswomen (b. 1686)
December 26 – Antonio Caldara, Italian composer (b. 1670)
Ahmed III, Ottoman Sultan (b. 1673)
Anna Colbjørnsdatter, Norwegian heroine (b. 1667)
John Porteous, Scottish captain (b. c. 1695)
Chen Shu, Chinese painter (b. 1660)
1736 (MDCCXXXVI) was a leap year starting on Sunday (dominical letter AG) of the Gregorian calendar and a leap year starting on Thursday (dominical letter DC) of the Julian calendar, the 1736th year of the Common Era (CE) and Anno Domini (AD) designations, the 736th year of the 2nd millennium, the 36th year of the 18th century, and the 7th year of the 1730s decade. As of the start of 1736, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923.