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|Centuries:||16th century – 17th century – 18th century|
|Decades:||1630s 1640s 1650s – 1660s – 1670s 1680s 1690s|
|Years:||1660 1661 1662 – 1663 – 1664 1665 1666|
|1663 by topic:|
|Arts and Science|
|Architecture - Art - Literature - Music - Science|
|Lists of leaders|
|Colonial governors - State leaders|
|Birth and death categories|
|Births - Deaths|
|Establishments and disestablishments categories|
|Establishments - Disestablishments|
|Ab urbe condita||2416|
|English Regnal year||14 Cha. 2 – 15 Cha. 2
— to —癸卯年十二月初三日
|- Vikram Samvat||1719–1720|
|- Shaka Samvat||1585–1586|
|- Kali Yuga||4764–4765|
|- Ǹrí Ìgbò||663–664|
|Japanese calendar||Kanbun 2
|Juche calendar||N/A (before 1912)|
|Julian calendar||Gregorian minus 10 days|
|Minguo calendar||249 before ROC
|Thai solar calendar||2206|
|Wikimedia Commons has media related to: 1663|
- January 10 – The Royal African Company is granted a Royal Charter by Charles II of England.
- March 5 – Emperor Go-Sai's reign ends and Emperor Reigen ascends to the throne of Japan.
- March 24 – King Charles II of England issues the Charter of Carolina, establishing the Province of Carolina and dividing it between eight Lords Proprietors.
- April 17 – The Turks declare war against Holy Roman Emperor Leopold I.
- May 7 – Opening of the Theatre Royal, Drury Lane, in London.
- June 8 – Battle of Ameixial: The Portuguese and some English auxiliaries defeat the Spanish.
- July 8 – King Charles II of England grants John Clarke a Royal Charter to the American Colony of Rhode Island and Providence Plantations.
- July 27 – The English Parliament passes the second Navigation Act, requiring that all goods bound for the American colonies have to be sent in English ships from English ports.
- August 21 – Concerned about the wintry weather, the Parliament of England holds an intercessary fast.
- August 28 – Severe frost in England.
Date unknown 
- The Prix de Rome Scholarship is established for students of the arts.
- The first Maroon community arises in Suriname.
- Robert Hooke discovers that cork is made of "tiny little rooms" which he first calls "Cells".
- February 1 – Mother Ignacia del Espiritu Santo, foundress (d. 1748)
- February 12 – Cotton Mather, American minister (d. 1728)
- February 25 – Pierre Antoine Motteux, French-born English dramatist (d. 1718)
- March 6 – Francis Atterbury, English bishop and man of letters (d. 1732)
- March 7 – Tomaso Antonio Vitali, Italian violinist and composer(d. 1745)
- March 22 – August Hermann Francke, German Protestant minister (d. 1727)
- May 20 – William Bradford, British-born printer (d. 1752)
- June 2 – Jean Baptiste Massillon, French churchman (d. 1742)
- August 31 – Guillaume Amontons, French physicist and instrument maker (d. 1705)
- October 16 – Prince Eugene of Savoy, French-born Austrian general (d. 1736)
- date unknown – William King, English poet (d. 1712)
- February 19 – Adam Adami, German bishop and diplomat (b. 1603)
- April 7 – Francis Cooke, Mayflower pilgrim (b. c. 1583)
- June 4 – William Juxon, Archbishop of Canterbury (b. 1582)
- June 25 – John Bramhall, Archbishop of Armagh and Anglican controversialist (b. 1594)
- July 7 – Thomas Baltzar, German violinist (b. c. 1631)
- September 18 – Joseph of Cupertino, Italian saint (b. 1603)
- October 20 – Raphael Cotoner, 60th Grandmaster of the Knights Hospitaller (b. 1601)
- December 5 – Severo Bonini, Italian composer (b. 1582)
- December 17 – Queen Nzinga of Ndongo and Matamba (b. c. 1583)
- December 28 – Francesco Maria Grimaldi, Italian mathematician and physicist (b. 1618)