1720s

• January 21 – Sweden and Prussia sign the Treaty of Stockholm (Great Northern War).
• 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.[1]
• February 24 – Battle of Nassau: Spanish forces assault the British settlement of Nassau, Bahamas during the War of the Quadruple Alliance.
• March 11 (February 29 Old Style) – 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 (March 24 Old Style) – The Riksdag of the Estates elects Frederick I new King of Sweden.

• 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.[2]
• 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.

• 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.

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