1664

January–June

• January 5 - Battle of Surat: Maratha Chhatrapati Shivaji defeats Mughal captain Inayat Khan, and sacks Surat.
• May 9 - Robert Hooke discovers Jupiter's Great Red Spot.
• June - Gazzetta di Mantova is first published in Mantua, Italy. It's the world's oldest private newspaper still published, and the oldest continuously published in print.
• June 9 - Kronenbourg Brewery is founded in Strasbourg.
• June - Siege of Novi Zrin : The Ottoman army besieges and destroys Novi Zrin fortress, in northern Croatia.

  July–December

• August 1 - Battle of Saint Gotthard: The Ottoman Empire is defeated by a Habsburg army, led by Raimondo Montecuccoli, leading to the Peace of Vasvár.
• August 27
• * The French East India Company is founded.
• * Peter Stuyvesant, Director-General of the Dutch colony of New Netherland, surrenders New Amsterdam to an English naval squadron, commanded by Colonel Richard Nicolls, without bloodshed. The English promptly rename the fledgling city New York, after the Duke of York.
• October 28 - The "Duke of York and Albany's maritime regiment of foot" is formed in London.
• October 31 - Surrounded by a Berber army, the French Navy evacuates the presidio of Jijel, conquered in June 12.

  Date unknown

• John Evelyn's Sylva, or A Discourse of Forest-Trees and the Propagation of Timber is published in London, in book form.

  Births

• January 1 - Alvise Pisani, 114th Doge of Venice
• January 4 - Lars Roberg, Swedish physician
• January 14
• * Johann Jakob Schudt, German theologian
• * Simon van Slingelandt, Grand Pensionary of Holland
• January 15 - Jean Meslier, French Catholic priest, later discovered to have promoted atheism
• January 17 - Antonio Salvi, Italian poet
• January 20 - Giovanni Vincenzo Gravina, Italian writer and jurist
• January 24 - John Vanbrugh, English architect and dramatist
• February 6 - Mustafa II, Ottoman Sultan
• February 8 - William Seymour, British politician
• February 13 - Teodor Andrzej Potocki, Polish noble
• February 23 - Georg Dietrich Leyding, German composer and organist
• February 24 - Thomas Newcomen, English inventor
• February 26 - Nicolas Fatio de Duillier, Swiss mathematician
• March 4 - Juan de Esteyneffer, Moravian German lay Jesuit missionary sent to the New World
• March 11 - Jørgen Otto Brockenhuus, Dano-Norwegian officer
• March 12 - Moritz Wilhelm, Duke of Saxe-Zeitz
• March 14 - Silvio Stampiglia, Italian poet and opera librettist
• March 17 - Georg Österreich, German composer and music collector
• March 20 - Johann Homann, German cartographer
• April 5 - Élisabeth Thérèse de Lorraine, French noblewoman, Princess of Epinoy by marriage
• April 6
• * Arvid Horn, Swedish politician
• * Gustaf Cronhielm, Swedish politician
• April 11 - Pierce Lewis, Welsh cleric who helped to "correct" the 1690 edition of the Welsh Bible
• April 14 - Ulrik Adolf Holstein, Danish nobleman and statesman
• April 30 - François Louis, Prince of Conti, French general
• May 6 - Bhai Bachittar Singh, Indian Sikh martyr
• May 10 - Tørres Christensen, Norwegian merchant
• May 20 - Andreas Schlüter, German architect and sculptor
• May 30 - Giulio Alberoni, Italian cardinal and statesman
• June 3 - Rachel Ruysch, painter from the Northern Netherlands
• June 7
• * Edward Harley, English politician
• * Henry Dawnay, 2nd Viscount Downe, Irish peer
• June 22 - Johann Ernst III, Duke of Saxe-Weimar
• June 24 - François Pourfour du Petit, French anatomist, ophthalmologist and surgeon
• June 28 - Nicolas Bernier, French composer
• July 3 - James Stanley, 10th Earl of Derby, English politician
• July 11 - James Ogilvy, 4th Earl of Findlater
• July 16 - Philippe Charles, Duke of Valois
• July 18 - Count Palatine Francis Louis of Neuburg, Hochmeister of the Teutonic Order
• July 21 - Matthew Prior, English poet and diplomat
• August 2 - Philip Reinhard, Count of Hanau-Münzenberg
• August 4 - Louis Lully, French composer
• August 12 - Magnus Stenbock, Swedish noble
• August 20 - János Pálffy, Hungarian field marshal, Palatine
• August 24
• * Christen Thomesen Sehested, Danish admiral
• * Willem Adriaan van der Stel, Dutch colonial administrator
• September 5
• * Charlotte Lee, Countess of Lichfield, illegitimate daughter of King Charles II of England
• * Vincenzo Ludovico Gotti, Italian Catholic cardinal
• * Louis Antoine de Pardaillan de Gondrin, French duke
• September 7
• * Johann Georg von Eckhart, German historian
• * Thomas Morgan, English politician
• September 9 - Johann Christoph Pez, German composer
• September 14 - John Blackadder, Scottish soldier
• September 18 - Anton Maria Maragliano, Italian artist
• October 3 - Giuseppe Alberti, Italian painter
• October 12 - Praskovia Saltykova, Russian tsarina
• October 16 - Abraham Alewijn, Dutch playwright
• October 18 - George Compton, 4th Earl of Northampton
• October 27 - Thomas Johnson, English politician
• October 31 - Sir Wilfrid Lawson, 2nd Baronet, of Isell, English politician
• November 9
• * Johann Speth, German composer
• * Henry Wharton, English writer
• November 12 - Marie-Jeanne L'Héritier, French writer
• November 16 - Louise Marie Thérèse, French Benedictine nun
• November 18 - Charles of Mecklenburg-Güstrow, Duke of Mecklenburg
• November 24 - Margherita Maria Farnese, Italian noblewoman
• December 10 - John Williams, American clergy
• December 13 - Countess Charlotte Johanna of Waldeck-Wildungen, German noblewoman
• December 15 - Azim-ush-Shan, Mughal prince
• December 17 - Henry Bayntun, English politician
• December 26 - Johann Melchior Dinglinger, German goldsmith
• date unknown - Johanna Dorothea Lindenaer, Dutch writer and agent
• * Catherine Jérémie, French-Canadian botanist
• * Maria Guyomar de Pinha, Siamese cook

  Deaths

• January 10 - Antoon Sanders, Dutch priest and historian
• January 14 - Françoise Madeleine d'Orléans, French princess
• January 27 - Archduke Charles Joseph of Austria, Roman Catholic bishop
• January 30 - Cornelis de Graeff, Dutch mayor
• February 16 - Sir John Trelawny, 1st Baronet, British baronet
• February 20 - Corfitz Ulfeldt, Danish statesman
• February 26 - Emmanuel Stupanus, Swiss physician
• March 7 - Bernhard von Mallinckrodt, German bibliophile
• March 16 - Ivan Vyhovsky, Ukrainian Cossack leader
• March 19 - Francisco de Araujo, Spanish theologian
• March 30 - Guru Har Krishan, 8th Guru of Sikhism
• March 31 - Charlotte Stanley, Countess of Derby, English defender of Latham House
• April 4 - Adam Willaerts, Dutch painter
• April 24 - Silvius I Nimrod, Duke of Württemberg-Oels
• May 19 - Elisabeth de Bourbon-Vendôme, French princess
• May 21 - Elizabeth Poole, Puritan and business woman
• June 1 - Michiel Sweerts, Flemish painter
• June 2 - Henry II, Duke of Guise
• June 22 - Katherine Philips, Anglo-Welsh poet
• July - Jan Janssonius, Dutch cartographer
• July 4 - George III of Brieg, Duke of Brzeg
• July 15 - Abraham Ecchellensis, Lebanese Maronite philosopher
• July 12 - Stefano della Bella, Italian printmaker
• July 16 - Andreas Gryphius, German writer
• July 19 - Egbert van der Poel, Dutch painter
• July 31 - Goschwin Nickel, Jesuit leader
• August 3 - Jacopo Vignali, Italian painter
• August 16 - Johannes Buxtorf II, Swiss theologian
• August 23 - Jean Bagot, French theologian
• August 24 - Maria Cunitz, Silesian astronomer
• August 27 - Francisco de Zurbarán, Spanish painter
• September 2 - Antoine de Laloubère, French Jesuit mathematician
• October 31 - William Frederick, Prince of Nassau-Dietz, Dutch stadtholder
• November 2 - George Ghica, Prince of Moldavia and Wallachia
• November 17 - Nicolas Perrot d'Ablancourt, Translator
• November 18 - Miklós Zrínyi, Croatian and Hungarian military leader, statesman
• December 15 - Dietrich Reinkingk, German lawyer and politician
• December 25 - Niccolò Ludovisi, Prince of Piombino
• December 26 - Eleonore Dorothea of Anhalt-Dessau, Duchess of Saxe-Weimar by marriage
• date unknown - Gu Mei, politically influential Chinese courtesan, poet and painter