1720

January–June

• January 21 - Sweden and Prussia sign the Treaty of Stockholm.
• February 17 - The Treaty of The Hague is signed between Spain, Britain, France, Austria and the Dutch Republic, ending the War of the Quadruple Alliance.
• February 24 - Battle of Nassau: Spanish forces assault the British settlement of Nassau, Bahamas during the War of the Quadruple Alliance.
• March 11 - Queen Ulrika Eleonora of Sweden resigns, to let her husband Frederick I take over as king of Sweden. She had desired a joint rule, in a similar manner to William III and Mary II in Britain, but as the Swedish Riksdag of the Estates refuses this, she abdicates in her husband's favour instead.
• April - "South Sea Bubble" in England: A scheme for the South Sea Company to take over most of the unconsolidated national debt of Britain massively inflates share prices.
• April 4 - The Riksdag of the Estates elects Frederick I new King of Sweden.

  July–December

• July 12 - "Bubble Act": the Lords Justice in Great Britain attempt to curb some of the excesses of the stock markets during the "South Sea Bubble". They dissolve a number of petitions for patents and charters, and abolish more than 80 joint-stock companies of dubious merit, but this has little effect on the creation of "Bubbles", ephemeral joint-stock companies created during the hysteria of the times.
• July 27 - The Battle of Grengam takes place in the Ledsund strait between the island communities of Föglö and Lemland. It was the last major naval battle in the Great Northern War that took place in the Åland Islands, marking the end of Russian and Swedish offensive naval operations in Baltic waters.
• August 14 - The Spanish Villasur expedition, which set out on June 16 from New Mexico, with the intention of checking French influence on the Great Plains of North America, ends in failure, as it is ambushed by a Pawnee and Otoe force.
• September - "South Sea Bubble": The English stock market crashes, with dropping prices for stock in the South Sea Company.
• November 16 - Pirate "Calico Jack" Rackham is brought to trial at Spanish Town in Jamaica; he is hanged at Port Royal two days later.

  Date unknown

• The Tuscarora people leave North Carolina as a result of European colonization.
• The Town on Queen Anne's Creek, North Carolina is renamed Edenton, in honor of North Carolina Governor Charles Eden; it is incorporated in 1722.
• The Guild Regulation of 1720 is introduced in Sweden.
• The Kangxi Emperor announces that all western businessmen in China can trade only in Guangzhou.
• Edmond Halley is appointed as Astronomer Royal for England.
• The Academia Real da Historia is founded in Lisbon, Portugal.
• Jonathan Swift begins major composition work on Gulliver's Travels in Ireland.
• Il teatro alla moda, a satirical pamphlet by Benedetto Marcello, is published anonymously in Venice.
• The first yacht club in the world, the Royal Cork Yacht Club, is founded in Ireland.

  Births

• January 2 - José de Gálvez, Spanish politician
• January 4 - Johann Friedrich Agricola, German composer
• January 13 - Richard Hurd, English bishop and writer
• January 27 - Samuel Foote, English dramatist and actor
• January 30 - Charles De Geer, Swedish industrialist, entomologist
• February 8 - Emperor Sakuramachi of Japan
• February 15 - Philippe Macquer, French historian
• March 9 - Philip Yorke, 2nd Earl of Hardwicke, English politician
• March 13 - Charles Bonnet, Swiss naturalist and writer
• March 22 - Nicolas-Henri Jardin, French architect
• April 23 - Vilna Gaon, Lithuanian rabbi
• May 8 - William Cavendish, 4th Duke of Devonshire, Prime Minister of the United Kingdom
• May 15 - Maximilian Hell, Slovakian astronomer
• July 18 - Gilbert White, English naturalist and cleric
• August 8 - Carl Fredrik Pechlin, Swedish politician
• August 12 - Konrad Ekhof, German actor
• August 18 - Laurence Shirley, 4th Earl Ferrers, English murderer
• August 30 - Samuel Whitbread, English brewer, politician
• October 3 - Johann Peter Uz, German poet
• October 4 - Giovanni Battista Piranesi, Italian artist
• October 8 - Jonathan Mayhew, American minister, patriot
• October 8 - Geneviève Thiroux d'Arconville, French novelist, translator and chemist
• October 19 - John Woolman, American Quaker preacher, abolitionist
• November 1 - Toussaint-Guillaume Picquet de la Motte, French admiral
• November 8 - Madeleine de Puisieux, French writer and active feminist
• November 16 - Carlo Antonio Campioni, French-born composer
• December 14 - Justus Möser, German statesman
• December 24 - Anna Maria Mozart, wife of Leopold Mozart and mother of Wolfgang Amadeus Mozart and Maria Anna Mozart
• December 26 - Gian Francesco Albani, Italian Catholic cardinal
• December 31 - Charles Edward Stuart, pretender to the British throne
• "date unknown" - Jane Gomeldon, English writer, poet and adventurer
• "date unknown" - Sheikh Lamech, Persian banker and accountant
• "date unknown" - Madame de Beaumer, French editor and writer

  Deaths

• January - Francis Daniel Pastorius, founder of Germantown, Pennsylvania
• January 4 - Harry Mordaunt, British politician
• January 10 - Ramon Perellos, Spanish 64th Grandmaster of the Knights Hospitaller
• January 12 - William Ashhurst, Lord Mayor of London
• January 19 - Eleonor Magdalene of Neuburg, Holy Roman Empress
• January 20
• * Giovanni Maria Lancisi, Italian physician
• * Angelo Paoli, Italian beatified
• January 31 - Thomas Grey, 2nd Earl of Stamford, English privy councilor
• February 4 - Robert Wroth, British politician
• February 27 - Samuel Parris, English-born Puritan minister
• March 6 - Pieter van Bloemen, Flemish painter
• March 13 - William Sewel, Dutch historian
• April 2 - Joseph Dudley, colonial Governor of Massachusetts
• April 12 - Balaji Vishwanath, Peshwa of the Maratha Empire
• April 20 - George Gordon, 1st Earl of Aberdeen, Lord Chancellor of Scotland
• April 21 - Antoine Hamilton, French writer
• June 19 - Robert Knox, English sea captain
• June 27 - Guillaume Amfrye de Chaulieu, French poet
• July 6 - Isaac Milles, English minister
• July 7 - Juan Romero de Figueroa, Spanish priest
• July 12 - King Sukjong of Joseon
• August 3
• * Anthonie Heinsius, Dutch politician
• * Anne Finch, Countess of Winchilsea, English poet
• August 9 - Simon Ockley, English orientalist
• August 17 - Anne Lefèvre, French scholar
• August 21 - John Leake, English Royal Navy admiral
• August 23 - Sybilla Masters, American inventor
• August 26 - Johann Christoph Volkamer, German botanist
• September 3 - Henri de Massue, Marquis de Ruvigny, 1st Viscount Galway, French soldier and diplomat
• September 9 - Philippe de Courcillon, French officer and author
• September 20 - Pierre de La Broue, American bishop
• October 10 - Antoine Coysevox, French sculptor
• November 18 - John Rackham, English pirate, also known as Calico Jack
• November 20 - Peder Tordenskjold, Norwegian naval hero
• November 27
• * Willem van Outhoorn, Dutch colonial governor
• * Diego de Salinas, Governor of Gibraltar
• December 29 – Maria Margarethe Kirch, German astronomer
• date unknown
• * Shahzada Assadullah Khan Abdali, Persian Governor of Herat
• * Demoiselle Conradi, German opera singer