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1677 was a common year starting on Friday of the Gregorian calendar and a common year starting on Monday of the Julian calendar, the 1677th year of the Common Era (CE) and Anno Domini (AD) designations, the 677th year of the 2nd millennium, the 77th year of the 17th century, and the 8th year of the 1670s decade. As of the start of 1677, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 1 – Jean Racine's tragedy Phèdre is first performed.
- January 21 – The first medical publication in America (a pamphlet on smallpox) is produced in Boston.
- February – The first arrest is made in the case, that will develop into the famous Affair of the Poisons.
- April 11 – Battle of Cassel: Philippe I, Duke of Orléans defeats William of Orange.
- April 16 – The Statute of Frauds is passed into English law.
- April 6 – Leopold I, Holy Roman Emperor visits the University of Innsbruck.
- May 29 – The Treaty of Middle Plantation establishes peace, between the Virginia colonists and the local Indians.
- May 31 – Scanian War – Battle of Møn: Danish ships clash with Swedish ships under Niels Juel, between Fehmarn and Warnemünde; the Danish defeat the Swedish, and capture a number of ships.
- June 25–June 26 – The Siege of Malmö is conducted.
- July 14 – Battle of Landskrona: Sweden defeats the Danes.
- August – The French guild of the Maitresses bouquetieres is founded in Paris.
- October 29 – Michel le Tellier becomes Chancellor of France.
- November 4 – The future Mary II of England marries William of Orange.
- November 16 – French troops occupy Freiburg.
- The Second London Baptist Confession of Faith is written (published in 1689).
- Spinoza's Ethics (Ethica, ordine geometrico demonstrata) is published as part of his Opera Posthuma in Amsterdam.
- Elias Ashmole gifts the collection, that begins the Ashmolean Museum, to the University of Oxford in England.
- Charles II of England makes Henry Purcell his court musician.
- Jules Hardouin Mansart begins la place Vendôme in Paris (it is completed in 1698).
- Francis Aungier, 3rd Baron Aungier of Longford, is created 1st Earl of Longford in the Peerage of Ireland.
- The John Roan School is established in Greenwich, London.
- Gottfried Wilhelm Leibniz gives a complete solution to the tangent problem.
- Antonie van Leeuwenhoek observes spermatozoa under the microscope.
- The use of male impotence is ended as a factor, in French divorce proceedings.
- Ice cream becomes popular in Paris.
- The population of Paris first exceeds 500,000.
- February 3 – Jan Santini Aichel, Czech architect (d. 1723)
- February 4 – Johann Ludwig Bach, German composer (d. 1731)
- February 8 – Jacques Cassini, French astronomer (d. 1756)
- May 4 – Françoise-Marie de Bourbon, youngest daughter of Louis XIV (d. 1749)
- August 27 – Otto Ferdinand von Abensperg und Traun, Austrian field marshal (d. 1748)
- September 17 – Stephen Hales, English physiologist, chemist, and inventor (d. 1761)
- October 20 – Stanisław Leszczyński, King of Poland (d. 1766)
- date unknown
- January 8 – Sir John Fowell, 2nd Baronet, English politician (b. 1623)
- January 18 – Jan van Riebeeck, Dutch founder of Cape Town (b. 1619)
- January 31 – Frederick VI, Margrave of Baden-Durlach (b. 1617)
- February 9 – George Horner, English politician (b. 1605)
- February 21 – Baruch Spinoza, Dutch philosopher (b. 1632)
- March 18 – Marie Luise von Degenfeld, morganatic second wife of Charles I Louis, Elector Palatine of Germany (b. 1634)
- March 28 – Václav Hollar, Czech-born actor (b. 1607)
- April 22 – Václav Eusebius František, Prince of Lobkowicz, Austrian field marshal and prince (b. 1609)
- May 4 – Isaac Barrow, English mathematician (b. 1630)
- May 20 – George Digby, 2nd Earl of Bristol, English statesman (b. 1612)
- May 22 – William, Margrave of Baden-Baden (b. 1593)
- May 23 – John, Count of Nassau-Idstein (1629–1677) (b. 1603)
- May 24 – Anders Bording, Danish writer (b. 1619)
- June 11 – Jacques Esprit, French writer (b. 1611)
- June 23 – Wilhelm Ludwig, Duke of Württemberg (b. 1647)
- June 18 – Johann Franck, German poet and hymnist (b. 1618)
- July 30 – Fabian von Fersen, Swedish soldier (b. 1626)
- July 11 – Timothy Turner, English judge, actor (b. 1585)
- July 27 – Johannes Loccenius, German historian (b. 1598)
- August 1 – George Christian, Landgrave of Hesse-Homburg (1669–1671) (b. 1626)
- August 20 – Pierre Petit, French astronomer, military engineer, and physicist (b. 1594)
- August 28 – Wallerant Vaillant, painter of the Dutch Golden Age (b. 1623)
- September 11 – James Harrington, English political philosopher (b. 1611)
- September 12
- October 9 – Gustav Adolph, Count of Nassau-Saarbrücken and general sergeant of the Holy Roman Empire at the Rhine (b. 1632)
- October 14 – Józef Bartłomiej Zimorowic, Polish poet (b. 1597)
- November 2 – Robert Sidney, 2nd Earl of Leicester, English politician (b. 1595)
- November 9 – Aernout van der Neer, Dutch painter (b. 1603)
- November 11
- November 14 – Matthias Abele, Austrian jurist, mine official (b. 1618)
- December 13 – Thomas Howard, 5th Duke of Norfolk, English noble (b. 1627)
- December 14 – Christian Albert, Burgrave and Count of Dohna, German nobleman and general in the army of Brandenburg (b. 1621)
- December 26 – Bernhard Gustav of Baden-Durlach, Swedish general, Prince-Abbot and cardinal (b. 1631)
- date unknown – Gilbert Sheldon, Archbishop of Canterbury (b. 1598)
- Kreyszig, Erwin. Differential Geometry. ISBN 978-0-486-66721-8.
- Grun, Bernard (1991). The Timetables of History: A Horizontal Linkage of People and Events. New York: Simon and Schuster. pp. 308–309.
Ice cream becomes popular as dessert in Paris