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1708 (MDCCVIII) was a leap year starting on Sunday (dominical letter AG) of the Gregorian calendar and a leap year starting on Thursday (dominical letter DC) of the Julian calendar, the 1708th year of the Common Era (CE) and Anno Domini (AD) designations, the 708th year of the 2nd millennium, the 8th year of the 18th century, and the 9th year of the 1700s decade. As of the start of 1708, 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 Wednesday, one day ahead of the Julian and ten days behind the Gregorian calendar.
- March 11 – Queen Anne withholds Royal Assent from the Scottish Militia Bill, the last time a British monarch vetoes legislation.
- March 23 – James Francis Edward Stuart, Jacobite pretender to the throne of Great Britain, unsuccessfully tries to land from a French fleet in the Firth of Forth in Scotland.
- July 1 – Tewoflos becomes Emperor of Ethiopia.
- July 11 – War of the Spanish Succession: Allied victory under the command of John Churchill, 1st Duke of Marlborough, against the French at the Battle of Oudenarde.
- August – The future Charles VI, Holy Roman Emperor weds Elisabeth Christine of Brunswick-Wolfenbüttel.
- August 18 – War of the Spanish Succession: Capture of Minorca by British forces.
- August 23 – Meidingu Pamheiba is crowned King of Manipur.
- August 29 – A native American attack in Haverhill, Massachusetts, kills 16 settlers.
- September 28 (O.S.); September 29 (Swedish calendar); October 9 (N.S.) – Battle of Lesnaya (Great Northern War): Peter the Great of Russia defeats the forces of the Swedish Empire.
- October 12 – War of the Spanish Succession: British forces capture Lille after a two-month siege, although the citadel continues to hold out for another six weeks.
- October 26 – Completion of the construction of St Paul's Cathedral in London.
- Kandahar is conquered by Mir Wais.
- Fearful of a Swedish attack, the Russians blow up the city of Tartu in Estonia.
- One third of the population of Masuria dies of the plague.
- Johann Sebastian Bach is appointed as chamber musician and organist at the court in Weimar.
- Italian philosopher Giambattista Vico delivers his inaugural lecture to the University of Naples, published as his first book, De Nostri Temporis Studiorum Ratione ("On the Order of the Scholarly Disciplines of Our Times"), in 1709.
- Calcareous hard-paste porcelain is produced for the first time in Europe at Dresden in Saxony by Ehrenfried Walther von Tschirnhaus and developed after his death (October) by Johann Friedrich Böttger.
- Merger (with consent of the Parliament of Great Britain) of the Company of Merchants of London Trading into the East Indies and the more recently established English Company Trading to the East Indies to form the United Company of Merchants of England Trading to the East Indies, known as the Honourable East India Company.
- January 25 – Pompeo Batoni, Italian painter (d. 1787)
- March 15 – John Hulse, Anglican priest (d. 1790)
- April 23 – Friedrich von Hagedorn, German poet (d. 1754)
- September 16 – Catharina Freymann, Norwegian pietist leader (d. 1791)
- October 16 – Albrecht von Haller, Swiss anatomist and physiologist (d. 1777)
- October 22 – Frederic Louis Norden, Danish explorer (d. 1742)
- November 15 – William Pitt, 1st Earl of Chatham, Prime Minister of the United Kingdom (d. 1778)
- December 8 – Francis I, Holy Roman Emperor (d. 1765)
- date unknown
- May 6 – François de Laval, first bishop of New France (b. 1623)
- May 11 – Jules Hardouin Mansart, French architect (b. 1646)
- May 12 – Adolphus Frederick II, Duke of Mecklenburg-Strelitz (b. 1658)
- June 30 – Emperor Tekle Haymanot I of Ethiopia (stabbed to death) (b. 1706)
- September 6 – Sir John Morden, 1st Baronet, English merchant and philanthropist (b. 1623)
- October 1 – John Blow, British composer (b. 1649)
- October 2 – Anne Jules de Noailles, French general (b. 1650)
- October 7 – Guru Gobind Singh, 10th Guru Sahib of Sikhism, Founder and Chief General of the Khalsa Army, social reformist, poet, and revolutionary (b. 1666)
- October 10 – David Gregory, Scottish astronomer (b. 1659)
- October 11 – Ehrenfried Walther von Tschirnhaus, German mathematician (b. 1651)
- October 22 – Hermann Witsius, Dutch theologian (b. 1636)
- October 24 – Seki Kōwa, Japanese mathematician (b. c. 1640)
- October 28 – Prince George of Denmark, consort of Anne, Queen of Great Britain (b. 1653)
- November 17 – Ludolf Bakhuizen, Dutch painter (b. 1631)
- December 22 – Hedwig Sophia, duchess of Holstein-Gottorp, Swedish writer (b. 1681)
- December 28 – Joseph Pitton de Tournefort, French botanist (b. 1656)
- Date unknown – Anna Maria Clodt, Swedish courtier (b. ?)
- Williams, Hywel (2005). Cassell's Chronology of World History. London: Weidenfeld & Nicolson. p. 292. ISBN 0-304-35730-8.
- Palmer, Alan; Veronica (1992). The Chronology of British History. London: Century Ltd. pp. 205–206. ISBN 0-7126-5616-2.
- "Stamps celebrate St Paul's with Wren epitaph". Evening Standard. Retrieved 2008-06-05.
- Landow, George P. (2010). "The British East India Company — the Company that Owned a Nation (or Two)". The Victorian Web. Retrieved 2011-11-22.