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1667 (MDCLXVII) was a common year starting on Saturday of the Gregorian calendar and a common year starting on Tuesday of the Julian calendar, the 1667th year of the Common Era (CE) and Anno Domini (AD) designations, the 667th year of the 2nd millennium, the 67th year of the 17th century, and the 8th year of the 1660s decade. As of the start of 1667, the Gregorian calendar was 10 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 20 – Russo-Polish War (1654-67): Poland cedes Kiev, Smolensk, and eastern Ukraine to Russia in the Treaty of Andrusovo, which puts a final end to Poland's status as a major Central European power.
- February – The first theatre in Scandinavia opens, in Lejonkulan and Bollhuset in Stockholm, Sweden.
- March – Louis XIV of France abolishes the livre parisis (Paris pound), in favor of the much more widely used livre tournois (Tours pound). He also designates Gabriel Nicolas de la Reynie as the first chief of "police" of Paris.
- March 27 – In North America (Canada), explorer René-Robert Cavelier, Sieur de La Salle is released from the Society of Jesus (Jesuits).
- April 6 – Dubrovnik earthquake: An earthquake in the Republic of Ragusa kills one fifth of the population.
- April 27 – The blind, impoverished, 58-year-old John Milton seals a contract for publication of Paradise Lost with London printer Samuel Simmons, for an initial payment of £5. The first edition is published in October and sells out in eighteen months.
- May 24 – The War of Devolution begins: France invades Flanders and Franche-Comté.
- June 9–14 – Raid on the Medway: A Dutch fleet under Admiral Michiel de Ruyter burns Sheerness, sails up the River Medway in England, raids Chatham Dockyard, and tows away the royal flagship The Royal Charles.
- June 15 – The first human blood transfusion is administered by Dr. Jean-Baptiste Denys. He transfuses the blood of a sheep to a 15-year-old boy (though this operation is a success, a later patient dies from the procedure and Denys is accused of murder).
- June 20 – Pope Clement IX succeeds Pope Alexander VII, becoming the 238th pope.
- June 26 – Louis XIV of France conquers Tournai.
- Mogul Emperor Aurangzeb buys off the warrior Shivaji, by making him a Rajah, and allowing him to collect taxes.
- Robert Hooke demonstrates that the alteration of the blood in the lungs is essential for respiration.
- The French army uses grenadiers.
- The first military campaign of Stenka Razin is conducted in Russia.
- Isaac Newton has investigated and written his works in subjects of optics, acoustics, the infinitesimal calculus, mechanism and thermodynamics. The researches themselves will be published only years later.
- April 29 – John Arbuthnot, English physician and writer (d. 1735)
- May 26 – Abraham de Moivre, French mathematician (d. 1754)
- June 18 – Ivan Trubetskoy, Russian field marshal (d. 1750)
- July 2 – Pietro Ottoboni, Italian cardinal (d. 1740)
- July 27 – Johann Bernoulli, Swiss mathematician (d. 1748)
- August 11 – Anna Maria Luisa de' Medici, last of the Medicis of Italy (d. 1743)
- September 5 – Giovanni Girolamo Saccheri, Italian mathematician (d. 1733)
- September 28 – Asano Naganori, Japanese warlord (d. 1701)
- November 2 – James Sobieski, Crown Prince of Poland (d. 1737)
- November 5 – Christoph Ludwig Agricola, German painter (d. 1719)
- November 30 – Jonathan Swift, Irish writer (d. 1745)
- December 9 – William Whiston, English mathematician (d. 1752)
- December 25 – Ehrengard Melusine von der Schulenburg, Duchess of Kendal and Munster (d. 1743)
- date unknown
- probable –
- January 28 – Maria Klara of Dietrichstein, German noblewoman (b. 1626)
- February 16 – Vincenzo Maculani, Italian Catholic cardinal (b. 1578)
- April 2 – Reinhold Curicke, jurist and historian from Danzig (Gda?sk) (b. 1610)
- April 10 – Jan Marek Marci, Bohemian physician and scientist (b. 1595)
- April 13 – Bassam Al-Soukaria, Lebanese army commander (b. 1580)
- April 21 – Roger Hill, English politician (b. 1605)
- April 24 – Matthew Wren, influential English clergyman (b. 1585)
- April 25 – Peter of Saint Joseph Betancur, Spanish saint and missionary to Guatemala (b. 1626)
- May 2 – George Wither, English writer (b. 1588)
- May 7 – Johann Jakob Froberger, German composer (b. 1616)
- May 10 – Marie Louise Gonzaga, Polish queen (b. 1611)
- May 14
- May 16
- May 22 – Pope Alexander VII (b. 1599)
- May 25 – Gustaf Bonde, Swedish statesman (b. 1620)
- May 26 – Albrecht von Kalckstein, German noble (b. 1592)
- May 28 – Jacques de Bela, French writer (b. 1586)
- June 5
- June 18 – Countess Louise Henriette of Nassau, Electress Consort of Brandenburg (b. 1627)
- June 19 – Anthony Günther, Count of Oldenburg (b. 1583)
- June 20 – James Stuart, Duke of Cambridge, British prince (b. 1663)
- July 4
- July 7 – Nicolas Sanson, French cartographer (b. 1600)
- July 11 – Stefano Durazzo, Italian cardinal (b. 1594)
- July 13 – Barthélemy Vimont, French missionary (b. 1594)
- July 28 – Abraham Cowley, English poet (b. 1618)
- August 3 – Francesco Borromini, Swiss sculptor and architect (b. 1599)
- August 8 – Frances Hyde, Countess of Clarendon, English noble (b. 1617)
- August 13
- August 28 – Jai Singh I, Maharaja of Jaipur (b. 1611)
- August 31 – Johann von Rist, German poet and dramatist known for the hymns he wrote (b. 1607)
- September 3 – Alonzo Cano, Spanish painter (b. 1601)
- September 10 – Erasmus Earle, English barrister and politician (b. 1590)
- September 20 – Niels Trolle, Governor General of Norway (b. 1599)
- September 24 – Michael Franck, German composer and poet (b. 1609)
- September 28 – Thomas Hall, English politician (b. 1619)
- September 29 – Herbert Morley, English politician (b. 1616)
- October 11 – Mattias de' Medici, Italian noble (b. 1613)
- October 18 – Emperor Fasilides of Ethiopia (b. 1603)
- October 24 – Godefroy Wendelin, Flemish astronomer (b. 1580)
- October 22 – Albert II, Margrave of Brandenburg-Ansbach, German prince (b. 1620)
- October 25 – Ernst Adalbert von Harrach, Austrian Catholic cardinal (b. 1598)
- November 12 – Hans Nansen, Danish statesman (b. 1598)
- November 19 – Robert Wallop, English politician (b. 1601)
- November 28 – Jean de Thévenot, French traveler and scientist (b. 1633)
- December 31 – Jerzy Sebastian Lubomirski, Polish noble (szlachcic) (b. 1616)
- date unknown – Antonio Abati, Italian poet