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 4 (March 24 Old Style) – The Riksdag of the Estates elects Frederick I new King of Sweden.
• 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.
• May 3 – The coronation of King Frederick I of Sweden takes place in Stockholm, six weeks after his rule began.
• May 20 – The Treaty of The Hague, signed between Spain and the Quadruple Alliance (Britain, France, the Netherlands and Austria) on February 17, goes into effect. Spain renounces its claims to the Italian possessions of the French throne, and Austria and the Duchy of Savoy trade Sicily for Sardinia.
• May 25 – The British privateer Speedwell, captained by George Shelvocke, is wrecked on the uninhabited island of Más a Tierra, the same island where Alexander Selkirk was marooned for five years; the island off of the coast of Chile is now called Robinson Crusoe Island. The crew is marooned for five months but is able to build a boat from timbers salvaged from the wreck, and is able to escape the island on October 6.
• June 1 – British silversmiths are once again allowed to use sterling silver after 24 years of being limited to lesser quality Britannia silver.
• June 11 – The British Parliament approves the Bubble Act (officially the Royal Exchange and London Assurance Corporation Act 1719), prohibiting the formation of joint-stock companies without prior approval by royal charter.
• June 19 – At Burhanpur (in what is now the Indian state of Madhya Pradesh), the Nizam-ul-Mulk of Hyderabad survives an attempted ambush by Mughal Empire forces dispatched by the Sayyid brothers (Syed Abdullah Khan and Syed Husain Ali Khan Barha) and goes on to establish a rival state in southern India.
• June 25 – The "South Sea Bubble", the phenomenal growth of the South Sea Company, reaches its peak as South Sea stock is priced at £1,060 a share. By the end of September, as panic sales are made, the price falls to £150.

• July 12 – Under the authority of the Bubble Act, the Lords Justices 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 14 – (July 3 O.S.) The Treaty of Frederiksborg is signed between Denmark and Sweden, ending the Great Northern War.
• 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 30 – "South Sea Bubble": The English stock market crashes, with dropping prices for stock in the South Sea Company. [3]

• October 8 – Sayyid Hussain Ali Khan Barha, one of the powerful Sayyid brothers of the Mughal Empire in India, is stabbed to death by Turkish nobleman Haider Beg Dughlat after Dughlat distracts him by giving him a petition to read. The assassination is ordered by Nizam ul-Mulk in retaliation for Sayyid Hussain's attempted ambush on June 19.
• October 15 – Muhammad Ibrahim, a grandson of the late Emperor Bahadur Shah I, is freed from prison by conspirators and declared the Mughal Emperor as a rival of his brother Muhammad Shah, beginning a 32-day reign that is described as being "like a drop of dew upon a blade of grass".
• November 13 – India's Mughal Emperor Muhammad Shah defeats his brother, pretender Muhammad Ibrahim in a battle at Hasanpur (in Uttar Pradesh). Ibrahim is returned to incarceration, kept at the citadel of Shahjahanabad, now part of Delhi.
• November 16 – Pirate "Calico Jack" Rackham is brought to trial at Spanish Town in Jamaica; he is hanged at Port Royal two days later.
• December 8 – Fath-Ali Khan Daghestani is deposed from his position as Grand Vizier of Iran (at the time, part of the Safavid Empire), is tortured by Mohammadqoli Khan, the bodyguard of the Safavid Shah, Sultan Husayn.

• 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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