1691

January–March

• January 6 – King William III of England, who rules Scotland and Ireland as well as being the Stadtholder of the Dutch Republic, departs from Margate to tend to the affairs of the Netherlands.
• January 14 – A fleet of ships carrying 827 Spanish Navy sailors and marines arrives at Manzanillo Bay on the island of Hispaniola in what is now the Dominican Republic and joins 700 Spanish cavalry, then proceeds westward to invade the French side of the island in what is now Haiti.
• January 15 – King Louis XIV of France issues an order specifically prohibiting play of games of chance, specifically naming basset and similar games, on penalty of 1,000 livres for the first offence.
• January 23 – Spanish colonial administrator Domingo Terán de los Ríos, most recently the governor of Sonora y Sinaloa on the east side of the Gulf of California, is assigned by the Viceroy of New Spain to administer a new province that governs lands on both sides of the Río Bravo del Norte, "Coahuila y Tejas", and effectively becomes the first Governor of Texas.
• February 13 – The Massachusetts Bay Colony issues the first paper money in North America, in lieu of coins, two months after a December 20 law authorizing the printing. The oldest known specimen, for 20 Massachusetts shillings bears the date "Feb. 3, 1690" based on the British old style calendar in use at the time.
• February 28 – An annular solar eclipse is visible across the Philippines, North Borneo and eastern Sumatra.
• March 5 – Nine Years' War: French troops under Marshal Louis-Francois de Boufflers besiege the Spanish-held town of Mons.
• March 14 – The Public Security Police Force of Macau is founded.
• March 17 – The Athenian Mercury begins twice-weekly publication by The Athenian Society in London.
• 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–June

• 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 Xuetas in Palma, Majorca. When 37 try to escape the island, they are burned alive at the stake.
• * The Province of New York establishes the New York Supreme Court as the Supreme Court of Judicature. It is the oldest Supreme Court with general original jurisdiction.
• May 16 – Jacob Leisler is hanged for treason.
• June – The first performance takes place of the semi-opera King Arthur with a libretto by John Dryden and music by Henry Purcell.
• June 23 – Ahmed II succeeds Suleiman II, as Ottoman Emperor.

  July–September

• July 12
• * Pope Innocent XII becomes the 242nd pope, succeeding Pope Alexander VIII.
• * Williamite War in Ireland – Battle of Aughrim: Protestant Williamite forces, led by Godert de Ginkell, decisively defeat Jacobites under the Marquis de St Ruth.
• August 11 – Battle of La Prairie in Canada: An English and Iroquois force come north from Albany, New York to attack Montreal, but are repulsed with significant casualties by the French and their First Nations allies.
• August 19 – The Battle of Slankamen takes place between the Ottoman Empire and the Holy Roman Empire and allies at Syrmia, and 25,000 Ottomans are killed, including Köprülüzade Fazıl Mustafa Pasha, the Grand Vizier.
• August 23 – A total solar eclipse is visible across South America, Central America and Mexico.
• August 27 – In Scotland, King William offers the Highland clans a pardon for their part in the Jacobite rising of 1689 if they agree to pledge allegiance to him before New Year's Day.
• September 3 – HMS Coronation and HMS Harwich are lost in a storm while making for shelter in Plymouth Sound with 900 killed.
• September 18 – War of the Grand Alliance: English and Dutch forces are defeated by the French in the Battle of Leuze.

  October–December

• October 3 – The Treaty of Limerick, ending the Williamite War in Ireland and guaranteeing civil rights to Roman Catholics, is signed. The Flight of the Wild Geese follows.
• October 17 – 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.
• November 26 – In Limerick, "A Form of Prayer and Thanksgiving to the Almighty God for the Preservation of Their Majesties, the Success of Their Forces in the reducing of Ireland, and for His Majesties Safe Return" is celebrated in all Anglican churches in Britain and Ireland by order of Archbishop Tillotson.
• December 6 – During the Morean War, Captain Luca Dalla Rocca of Naples betrays Venice by surrendering the fortress of Gramvousa, on the island of Crete to the Ottoman Turks, in return for a large amount of money and sanctuary in Istanbul.
• December 22 – Patrick Sarsfield and 19,000 troops of the Irish Army who had been supporters of the Jacobite Rebellion leave the country and relocate to France.

  Date unknown

• HMNB Devonport, currently one of three operating bases in the United Kingdom for the Royal Navy and the largest naval base in Western Europe, opens.
• Michel Rolle invents Rolle's theorem, which states that any real-valued differentiable function that attains equal values at two distinct points must have at least one stationary point somewhere between them.
• The Khalkha submit to the Manchu invaders, bringing most of modern-day Mongolia under the rule of the Qing Dynasty.
• Nimavar school in Isfahan, Iran is built and opens in this era of Suleiman I.
• The textile factory Barnängens manufaktur is founded in Stockholm, Sweden.
• The Society for the Reformation of Manners is founded in the London Borough of Tower Hamlets with the aim of suppressing profanity, immorality, and other lewd activities in general, and of brothels and prostitution in particular.