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was a common year starting on Thursday of the Gregorian calendar and a common year starting on Sunday of the Julian calendar, the 1665th year of the Common Era (CE) and Anno Domini (AD) designations, the 665th year of the 2nd millennium, the 65th year of the 17th century, and the 6th year of the 1660s decade. As of the start of 1665, the Gregorian calendar was
10 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 5 – The Journal des sçavans begins publication in France, the first scientific journal.
- March 4 – The Second Anglo-Dutch War begins.
- March 6 – The Philosophical Transactions of the Royal Society begins publication, the first scientific journal in English.
- March 11 – A new legal code is approved for the Dutch and English towns of New York, guaranteeing all Protestants the right to continue their religious observances unhindered.
- March 16 – Bucharest allows Jews to settle in the city, in exchange for an annual tax of 16 guilders.
- April 12 – Margaret Porteous is the first person recorded to die in the Great Plague of London. This last major outbreak of Bubonic plague in the British Isles has possibly been introduced by Dutch prisoners of war since 1331 in China. Two-thirds of Londoners leave the city, but over 68,000 die. The plague spreads to Derbyshire.
- May 19 – Great fire of Newport, Shropshire, England.
- June 12 – England installs a municipal government in New York City (the former Dutch settlement of New Amsterdam).
- June 13 (June 3 O.S.) – Second Anglo-Dutch War: The English naval victory at the Battle of Lowestoft under James Stuart, Duke of York.
- June 30 – King Charles II of England issues a second charter for the Province of Carolina, which clarifies and expands the borders of the Lords Proprietors' tracts.
- July 3 – The first documented case of cyclopia is found in a horse.
- July 7 – King Charles II of England leaves London with his entourage, fleeing the Great Plague. He moves his court to Salisbury, then Exeter.
- August – The Great Plague forces the closure of the University of Cambridge, where Isaac Newton is a student. Newton retires to his home in Lincolnshire for safety, and stays there for two years. During that time alone, Newton will make groundbreaking discoveries in mathematics, calculus, mechanics, and optics, and lay the foundations for his books Philosophiæ Naturalis Principia Mathematica and Optiks.
- August 2 – Second Anglo-Dutch War: The Dutch fleet defeats the English in the Battle of Vågen.
- August 27 – Ye Bare & Ye Cubbe, the first play in English in the American colonies, is performed in Pungoteague, Virginia.
- September – Robert Hooke's Micrographia is published in London, first applying the term 'cell' to plant tissue, which he discovered first in cork, then in living organisms, using a microscope.
- September 17 – Charles II of Spain becomes king, while not yet four years old.
- September 22 – Molière's L'Amour médecin is first presented, before Louis XIV of France, at the Palace of Versailles, with music by Jean-Baptiste Lully.
- October 5 – The University of Kiel is founded.
- October 21 – Louis XIV of France and Jean-Baptiste Colbert found the Manufacture royale des glaces of Saint Gobain, which is the oldest French company of the CAC 40, with 350 years in 2015.
- October 29 – Battle of Mbwila: Portuguese forces defeat and kill King António I of Kongo.
- November 7 – The London Gazette, the oldest surviving journal, is first published as The Oxford Gazette.
- December 10 – The Royal Netherlands Marine Corps is founded by Michiel de Ruyter.
- February 6 – Anne, Queen of Great Britain (d. 1714)
- February 12 – Rudolf Jakob Camerarius, German botanist and physician (d. 1721)
- March 4 – Philip Christoph von Königsmarck, Swedish soldier (d. 1694)
- March 17 – Élisabeth Jacquet de La Guerre, French harpsichordist and composer (d. 1729)
- April 19 – Jacques Lelong, French bibliographer (d. 1721)
- April 29 – James Butler, 2nd Duke of Ormonde, Irish statesman and soldier (d. 1745)
- June 4 – Zacharie Robutel de La Noue, Canadian soldier (d. 1733)
- July 2 – Samuel Penhallow, English-born American colonist, historian (d. 1726)
- August 21 – Giacomo F. Maraldi, French-Italian astronomer (d. 1729)
- August 27 – John Hervey, 1st Earl of Bristol, English politician (d. 1751)
- December 25 – Lady Grizel Baillie, Scottish songwriter (d. 1746)
- December 28 – George FitzRoy, 1st Duke of Northumberland, English general (d. 1716)
- date unknown – Ingeborg i Mjärhult, Swedish soothsayer (d. 1749)
- January 1 – Christian William of Brandenburg, administrator of the bishoprics of Magdeburg and Halberstadt (b. 1587)
- January 4 – Herman Fortunatus, Margrave of Baden-Rodemachern (b. 1595)
- January 11 – Louise de La Fayette, French courtier, friend of King Louis XIII (b. 1618)
- January 12 – Pierre de Fermat, French mathematician (b. 1601)
- January 29 – Jeanne des Anges, French Ursuline nun in Loudun (b. 1602)
- January 31 – Johannes Clauberg, German theologian and philosopher (b. 1622)
- March 1 – Thomas Wentworth, 5th Baron Wentworth, English baron and politician (b. 1612)
- March 11 – Clemente Tabone, Maltese landowner and militia member (b. c. 1575)
- March 15 – Christian Louis, Duke of Brunswick-Lüneburg (b. 1622)
- April 21 – Jean-Joseph Surin, French Jesuit writer (b. 1600)
- May 1 – Francis Mansell, English academic (b. 1579)
- May 24 – Mary of Jesus of Ágreda, Franciscan abbess and spiritual writer (b. 1602)
- May 31 – Pieter Jansz. Saenredam, Dutch painter (b. 1597)
- June 3
- June 6 – George Christian, Prince of East Frisia, prince of Ostfriesland (b. 1634)
- June 13 – Egbert Bartholomeusz Kortenaer, Dutch admiral (b. 1604)
- June 17 – Maria Elisabeth of Holstein-Gottorp, Landgravine of Hesse-Darmstadt (b. 1634)
- June 25 – Sigismund Francis, Archduke of Austria, regent of Tyrol and Further Austria (b. 1630)
- July 11 – Kenelm Digby, English privateer (b. 1603)
- July 18 – Stefan Czarniecki, Polish general (b. 1599)
- July 27 – Francesco Cairo, Italian painter (b. 1607)
- July 28 – Louis Giry, French lawyer, classical scholar (b. 1596)
- August 14 – Charles II, Duke of Mantua and Montferrat, son of Charles of Gonzaga-Nevers of Rethel (b. 1629)
- August 28 – Elisabetta Sirani, Italian painter (b. 1638)
- September 1 – Walter Erle, English politician (b. 1586)
- September 2 – Juan Alonso de Cuevas y Davalos, Roman Catholic prelate, Archbishop of Mexico and Antequera (b. 1590)
- September 12 – Jean Bolland, Flemish Jesuit writer (b. 1596)
- September 17 – King Philip IV of Spain (b. 1605)
- September 25 – Maria Anna of Austria, Electress of Bavaria (b. 1610)
- October 22 – César, Duke of Vendôme, French nobleman (b. 1594)
- November 1 – Sir John Perceval, 1st Baronet, Irish nobleman (b. 1629)
- November 10 – Samuel Capricornus, Czech composer (b. 1628)
- November 17 – John Earle (bishop), English bishop (b. 1601)
- November 19 – Nicolas Poussin, French painter (b. 1594)
- November 20 – Julius Henry, Duke of Saxe-Lauenburg (b. 1586)
- November 24 – Simon Le Moyne, French missionary (b. 1604)
- December 2
- December 10 – Tarquinio Merula, Italian composer (b. c. 1594)
- December 29 – George Wilde, Irish bishop (b. 1610)