Year 1691 (MDCXCI) was a common year starting on Monday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Thursday of the 10-day slower Julian calendar).

Events of 1691

January - June

• March 5 - Nine Years' War: French troops under Marshal Louis-Francois de Boufflers besiege the Spanish-held town of Mons.
• March 20 - Leisler's Rebellion: A new governor arrives in New York - Jacob Leisler surrenders after a standoff of several hours.
• March 29 - The Siege of Mons ends in the city’s surrender.
• April 9 - A fire at the Palace of Whitehall in London destroys its Stone Gallery.
• May 6 - The Spanish inquisition condemns and forcibly baptizes 219 Jews in Palma Majorca. When 37 try to escape the island, they are burned alive at the stake.
• May 16 - Jacob Leisler is hanged for treason.
• June - Ahmed II (1691-1695) succeeds Suleiman II (1687-1691) as emperor of the Ottoman Empire.

July - December

• July 12
  • Pope Innocent XII succeeds Pope Alexander VIII as the 242nd pope.
  • Battle of Aughrim: Williamite troops defeat the Jacobites in Ireland.
• October 3 - The Treaty of Limerick, which guarantees civil rights to Catholics, is signed. (It was broken "before the ink was dry")

Undated

• Michel Rolle invents Rolle's theorem, an essential theorem of mathematics.
• In New England the two separate colonies of Massachusetts Bay Colony and Plymouth Colony are united into a single entity by an act of the King and Queen of England.
• The Khalkha submit to the Manchu invaders, bringing most of modern-day Mongolia under the rule of the Qing dynasty.

Births

• February 27 - Edward Cave, English editor and publisher (d. 1754)
• April 5 - Louis VIII, Landgrave of Hesse-Darmstadt (d. 1768)
• April 9 - Johann Matthias Gesner, German classical scholar (d. 1761)
• June 17 - Giovanni Paolo Pannini, Italian painter and architect (d. 1765)
• August 25 - Alessandro Galilei, architect and mathematician (d. 1736)
• September 29 - Richard Challoner, English Catholic prelate (d. 1781)
• October 1 - Arthur Onslow, English politician (d 1768)
• October 28 - Peder Tordenskjold, Norwegian naval hero (d. 1720)

Deaths

• January 13 - George Fox, English founder of the Society of Friends (b. 1624)
• January 17 - Richard Lower, English physician (b. 1631)
• February 1 - Pope Alexander VIII (b. 1610)
• April 3 - Jean Petitot, Swiss enamel painter (b. 1607)
• May 11 - Colonel John Birch, English soldier (b. 1615)
• May 16 - Jacob Leisler, German-born American colonist (b. 1640)
• May 23 - Adrien Auzout, French astronomer (b. 1622)
• May 29 - Cornelis Tromp, Dutch admiral (b. 1629)
• June 23 - Suleiman II, Sultan, Ottoman Empire (b. 1642)
• July 12 - Marquis de St Ruth (killed at the Battle of Aughrim)
• July 16 - François-Michel le Tellier, Marquis de Louvois, French war minister (b. 1641)
• July 30 - Daniel Georg Morhof, German writer and scholar (b. 1639)
• August 14 - Richard Talbot, 1st Earl of Tyrconnel, Irish rebel (b. 1630)
• September 12 - John George III, Elector of Saxony (b. 1647)
• October 9 - William Sacheverell, English statesman (b. 1638)
• October 10 - Isaac de Benserade, French poet (b. 1613)
• November 14 - Tosa Mitsuoki, Japanese painter (b. 1617)
• November 15 - Aelbert Cuyp, Dutch painter (b. 1620)
• December 8 - Richard Baxter, English clergyman (b. 1615)
• December 30 - Robert Boyle, Irish chemist (b. 1627)
• probable - Elizabeth Polwheele, English playwright (b. c. 1651)