1513

Year 1513 (MDXIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

January–June

 * March 11 – Pope Leo X (layman Giovanni di Lorenzo de' Medici) succeeds Pope Julius II, as the 217th pope, despite a strong challenge by Italian cardinal Raffaele Riario and his group of seniors, or cardinals that were elected by Sixtus IV and Innocent VIII, who were opposed to the relatively newer juniors that included Medici.
 * March 27 – Juan Ponce de León becomes the first European definitely known to sight Florida, mistaking it for another island.
 * April 2
 * Juan Ponce de León and his expedition become the first Europeans known to visit Florida, landing somewhere on the east coast.
 * Juan Garrido (as part of Juan Ponce de León's expedition) becomes the first African known to visit North America, landing somewhere on the east coast of Florida.
 * May – Portuguese explorer Jorge Álvares lands on Lintin Island, in the Pearl River estuary.
 * June 6 – Italian Wars – Battle of Novara: Swiss mercenaries defeat the French under Louis II de la Trémoille, forcing the French to abandon Milan and Italy.

July–December

 * July 22 – Christian II becomes King of Denmark and Norway.
 * August 16
 * Battle of Dubica (part of the Hundred Years' Croatian–Ottoman War): Croatian troops under Petar Berislavić, Ban (Viceroy) of Croatia, defeat an Ottoman army under Sanjak-bey Junuz-aga
 * Battle of the Spurs (or Battle of Guinegate, part of the War of the League of Cambrai): English and allied troops under Henry VIII defeat French cavalry under Marshal La Palice.
 * August 23 – Thérouanne is given to Henry VIII of England after a treaty is concluded in the aftermath of the Battle of the Spurs.
 * September – The dispute between Johann Reuchlin and Johannes Pfefferkorn concerning the Talmud and other Jewish books, is referred to Pope Leo X.
 * September 9
 * Battle of Flodden: King James IV of Scotland is defeated and killed by an English army under Thomas Howard, Earl of Surrey. James's son, the Duke of Rothesay, becomes James V, King of Scots.
 * Johann Reuchlin is summoned for an inquisition trial, which was initiated by Jacob van Hoogstraaten. The verdict of the trial was never revealed, as when it was going to be announced on October 12, the archbishop of Mainz ordered the court to go into recess on threat of resigning the court, and the trial never went on.  Eventually, in March 1514, an ecclesiastical court presided over by George, Bishop of Speyer cleared Reuchlin of any charges and ordered Hoogstraten to pay the cost of 111 guldens,  although this was overturned by Leo X in a papal decision in 1520.
 * September 25 – Vasco Núñez de Balboa, first sees what will become known as the Pacific Ocean from the Isthimus of Darién. This moment is later referenced in a poem by John Keats called "On First Looking into Chapman's Homer" with the line "silent upon a peak in Darién" although he mistakenly references Hernán Cortés as the one who saw the Pacific from Darién.
 * September 30 – A major rock avalanche occurs in the Southern side of the Swiss Alps at Monte Crenone, which destroys the village of Biasca, floods Bellinzona, and formed a lake of 390 m.a.s.l.
 * October 7 – Battle of La Motta (War of the League of Cambrai): Spanish troops under Ramón de Cardona decisively defeat those of the Republic of Venice under Bartolomeo d'Alviano in Schio.
 * December – Louis XII of France makes peace with the Pope. He attempts to make peace with Spain by offering King Ferdinand his daughter Renée to one of his grandsons along with renouncing his claims on Naples, but the proposal was never accepted.
 * December 17 – Appenzell becomes a member of the Swiss Confederacy.

Undated

 * Niccolò Machiavelli is suspected of trying to overthrow the House of Medici and is arrested and tortured. He is soon after released and he moves to his farm in San Casciano, and he writes The Prince.
 * Leo Africanus visits Timbuktu, second city of the Songhai Empire.
 * Paracelsus begins studying at Ferrara University.

Births

 * February 14 – Domenico Ferrabosco, Italian composer (d. 1573)
 * March 15 – Hedwig Jagiellon, Electress of Brandenburg (d. 1573)
 * April 22 – Tachibana Dōsetsu, Japanese Daimyō (d. 1585)
 * June 10 – Louis, Duke of Montpensier (1561–1582) (d. 1582)
 * August 3 – John, Margrave of Brandenburg-Küstrin (d. 1571)
 * September 23 – Hans Buser, Swiss noble (d. 1544)
 * September 24 – Catherine of Saxe-Lauenburg, queen of Gustav I of Sweden (d. 1535)
 * October 30 – Jacques Amyot, French writer (d. 1593)
 * December 3 – Lorenzo Strozzi, Italian Catholic cardinal (d. 1571)
 * December 23 – Thomas Smith, English scholar and diplomat (d. 1577)
 * date unknown
 * Abe Motozane, Japanese general (d. 1587)
 * Anna Hogenskild, Swedish lady-in-waiting (d. 1590)
 * Michael Baius, Belgian theologian (d. 1589)
 * George Cassander, Flemish theologian (d. 1566)
 * Thomas FitzGerald, 10th Earl of Kildare (d. 1537)
 * Elisabeth Plainacher, Austrian alleged witch (d. 1583)

Deaths

 * January – Hans Folz, German author (b. c. 1437)
 * January 20 – Helena of Moscow, Grand Duchess consort of Lithuania and queen consort of Poland (b. 1476)
 * February 20 – King John of Denmark, Norway, and Sweden (b. 1455)
 * February 21 – Pope Julius II (b. 1443)
 * March 10 – John de Vere, 13th Earl of Oxford, English general (b. 1443)
 * April 24 – Şehzade Ahmet, oldest son of Sultan Bayezid II (executed) (b. 1465)
 * April 30 – Edmund de la Pole, 3rd Duke of Suffolk, Duke of Suffolk (b. 1471)
 * August 3 – Ernst II of Saxony, Archbishop of Magdeburg (1476–1513) and Administrator of Halberstadt (b. 1464)
 * September 9 (killed at the Battle of Flodden)
 * James IV of Scotland (b. 1473)
 * George Douglas, Master of Angus (b. 1469)
 * William Douglas of Glenbervie (b. 1473)
 * William Graham, 1st Earl of Montrose, Scottish politician (b. 1464)
 * George Hepburn, Scottish bishop
 * Adam Hepburn, 2nd Earl of Bothwell, Scottish politician, Lord High Admiral of Scotland
 * Adam Hepburn of Craggis
 * David Kennedy, 1st Earl of Cassilis, Scottish soldier (b. 1478)
 * Alexander Lauder of Blyth, Scottish politician
 * Alexander Stewart, Scottish archbishop (b. 1493)
 * Matthew Stewart, 2nd Earl of Lennox, Scottish politician (b. 1488)
 * October 27 – George Manners, 11th Baron de Ros, English nobleman
 * date unknown
 * Claudine de Brosse, duchess Consort of Savoy (b. 1450)
 * Hua Sui, Chinese inventor and printer (b. 1439)