|Covid-19|January 25–26 – Apalachee massacre: English colonists from the Province of Carolina and their native allies stage a series of brutal raids against a largely pacific population of Apalachee in Spanish Florida.
February 29 – Raid on Deerfield (Queen Anne's War): French Canadians and Native Americans sack Deerfield, Massachusetts, killing over 50 English colonists.
February – In America, Mardi Gras is celebrated with the Masque de la Mobile in the capital of Louisiana (New France), Mobile, Alabama.
April 21 – Battle of Biskupice between the Hungarians (Kurucs) and Danes.
April 24 – The first regular newspaper in the Thirteen Colonies of British North America, The Boston News-Letter, is published.
May 28 – Battle of Smolenice: Kuruc rebels defeat the Austrian army and its allies.
June 13 – Battle of Koroncó: Austrians and their allies from Denmark, Prussia, Croatia, Germany and Vojvodina defeat the Kurucs.
July – Daniel Defoe documents the Great Storm of 1703 in England with eyewitness testimonies in The Storm.
July 12 – Great Northern War – King Charles XII of Swedish forces the election of his ally Stanisław Leszczyński as King of Poland in place of Augustus II the Strong.
August 3 (July 23 Old Style) – War of the Spanish Succession – Capture of Gibraltar from Spain by English and Dutch forces under Sir George Rooke.
August 13 (August 2 OS) – War of the Spanish Succession – Battle of Blenheim: Allied troops under John Churchill, Earl of Marlborough and Prince Eugene of Savoy defeat the Franco-Bavarian army.
August 24 (August 13 OS) – War of the Spanish Succession – French and English fleets clash off Málaga, causing heavy casualties in both sides but without sinking any ships.
September – War of the Spanish Succession – The Twelfth Siege of Gibraltar by French and Spanish troops begins.
Great Northern War: Russian troops under Tsar Peter the Great capture Tartu and Narva.
The Sultanate of Brunei cedes its north-east territories to the Sultanate of Sulu.
The lower three counties of the Province of Pennsylvania become the colony of Delaware.
An earthquake strikes Gondar in Ethiopia.
A Tale of a Tub, the first major satire by Jonathan Swift (written 1694–1697), is published in London, running through three editions this year.
Isaac Newton publishes his Opticks.
The Students' Monument is built in Aiud, Romania.
Rome decrees that Roman ceremonial practice in Latin (not in Chinese) is to be the law for Chinese missions.
Thomas Darley purchases the bay Arabian horse Darley Arabian in Aleppo, Syria, and ships him to stud in England where he becomes the most important foundation sire of all modern thoroughbred racing bloodstock.
January 1 – Soame Jenyns, English writer (d. 1787)
February 12 – Charles Pinot Duclos, French writer (d. 1772)
February 28 – Louis Godin, French astronomer (d. 1760)
April 10 – Benjamin Heath, English classical scholar (d. 1766)
June 4 – Benjamin Huntsman, English inventor and manufacturer (d. 1776)
June 11 – Carlos Seixas, Portuguese composer (d. 1742)
June 17 – John Kay, English inventor (d. 1780)
June 22 – John Taylor, English classical scholar (d. 1766)
June 24 – Jean-Baptiste de Boyer, Marquis d'Argens, French writer (d. 1771)
July 15 – August Gottlieb Spangenberg, German religious leader (d. 1792)
July 31 – Gabriel Cramer, Swiss mathematician (d. 1752)
October 29 – John Byng, British admiral (d. 1757)
November 1 – Paul Daniel Longolius, German encyclopedist (d. 1779)
December 29 – Martha Daniell Logan, American botanist (d. 1779)
December 31 – Carl Gotthelf Gerlach, German organist (d. 1761)
February 2 – Guillaume François Antoine, Marquis de l'Hôpital, French mathematician (b. 1661)
February 25 – Isabella Leonarda, Italian composer (d. 1620)
February 23 – Georg Muffat, German composer (b. 1645)
February 24 – Marc-Antoine Charpentier, French composer (b. 1643)
March 17 – Menno van Coehoorn, Dutch military engineer (b. 1641)
April 8 – Hiob Ludolf, German orientalist (b. 1624)
April 8 – Henry Sydney, 1st Earl of Romney, English statesman (b. 1641)
April 10 – William Egon of Fürstenberg, Bishop of Strassburg (b. 1629)
April 12 – Jacques-Bénigne Bossuet, French bishop and writer (b. 1627)
April 15 – Johann van Waveren Hudde, Dutch mathematician (b. 1628)
April 20 – Agnes Block, Dutch horticulturalist (b. 1629)
May 3 – Heinrich Ignaz Franz Biber, Austrian composer (b. 1644)
May 13 – Louis Bourdaloue, French Jesuit preacher (b. 1632)
June 18 – Tom Brown, English satirist (b. 1662)
June 30 – John Quelch, English pirate (b. 1666)
July 3 – Sofia Alekseyevna of Russia, regent (b. 1657)
July 7 – Pierre-Charles Le Sueur, French fur trader and explorer (b. c. 1657)
July 20 – Peregrine White, first English child born in the Massachusetts Bay Colony (b. 1620)
July 22 – Selim I Giray, Crimean khan
August 14 – Roland Laporte, French Protestant leader (b. 1675)
August 19 – Jane Leade, English Christian mystic (b. 1624)
October 28 – John Locke, English philosopher (b. 1632)
November 4 – Andreas Acoluthus, German orientalist (b. 1654)
1704 (MDCCIV) was a leap year starting on Tuesday (dominical letter FE) of the Gregorian calendar and a leap year starting on Saturday (dominical letter BA) of the Julian calendar, the 1704th year of the Common Era (CE) and Anno Domini (AD) designations, the 704th year of the 2nd millennium, the 4th year of the 18th century, and the 5th year of the 1700s decade. As of the start of 1704, the Gregorian calendar was 11 days ahead of the Julian calendar, which remained in localized use until 1923. In the Swedish calendar it was a leap year starting on Friday, one day ahead of the Julian and ten days behind the Gregorian calendar.