|Ab urbe condita||1766|
|Balinese saka calendar||934–935|
|English Regnal year||N/A|
|Chinese calendar||壬子年 (Water Rat)|
3709 or 3649
— to —
癸丑年 (Water Ox)
3710 or 3650
|- Vikram Samvat||1069–1070|
|- Shaka Samvat||934–935|
|- Kali Yuga||4113–4114|
|Japanese calendar||Chōwa 2|
|Minguo calendar||899 before ROC|
|Seleucid era||1324/1325 AG|
|Thai solar calendar||1555–1556|
1139 or 758 or −14
— to —
1140 or 759 or −13
|Wikimedia Commons has media related to 1013.|
- King Henry II of Germany signs a peace treaty at Merseburg with Duke Bolesław I (the Brave) of Poland. As part of the treaty, Bolesław pays homage and recognizes Henry as his overlord in exchange for receiving the March of Lusatia (including the town of Bautzen) and the March of Meissen as fiefs. To seal their peace, Bolesław's son Mieszko II marries Richeza of Lotharingia (granddaughter of the late Emperor Otto II).
- Sulayman ibn al-Hakam reconquers the Caliphate of Córdoba in Al-Andalus (modern Spain) and deposes Hisham II. Sulayman becomes the fifth Umayyad caliph of Córdoba (until 1016).
- Winter – Henry II (anxious to be crowned as Holy Roman Emperor) mobilises a German expeditionary army at Augsburg, to begin his second Italian military campaign.
- Summer – Danish Viking raiders led by Sweyn Forkbeard (accompanied by his son Cnut) sail from Denmark to attack England. Again London defends itself and the Vikings move elsewhere, plundering Wessex, Mercia and Northumbria. King Æthelred II (the Unready) sends his sons Edward and Alfred to Normandy. Æthelred retreats to the Isle of Wight and follows them later into exile.
- December 25 – Sweyn Forkbeard takes control of the Danelaw and is proclaimed king of England in London. Some of the English provinces refuse to pay homage to Sweyn, who has no dynastic right to claim the throne.
- The Four Great Books of Song, the Song Dynasty Chinese encyclopedia Prime Tortoise of the Record Bureau (which had been compiled since 1005), is completed in 1,000 volumes of 9.4 million written Chinese characters.
- Kaifeng, capital of China, becomes the largest city of the world, taking the lead from Córdoba in Al-Andalus (modern Spain).
- Abu al-Qasim al-Zahrawi (called father of surgery) dies. He writes Al-Tasrif (The Method of Medicine), a 30-part medical encyclopedia in Arabic. Introducing his collection of over 200 surgical instruments.
- July 18 – Hermann of Reichenau, German music theorist (d. 1054)
- August 15 – Teishi (Yōmeimon-in), Japanese empress (d. 1094)
- Abu al-Walid al-Baji, Moorish scholar and poet (d. 1081)
- Guaimar IV, Italian nobleman (approximate date)
- Isaac Alfasi, Algerian Talmudist and posek (d. 1103)
- Richeza (or Adelaide), queen of Hungary (d. 1075)
- April 19 – Hisham II, caliph of Córdoba (Spain) (b. 966)
- June 5 – Al-Baqillani, Arab theologian, jurist and logician
- Al-Mahdi al-Husayn, Zaidi imam of Yemen (b. 987)
- Abu al-Qasim al-Zahrawi, Arab physician and surgeon (b. 936)
- Giselbert I, count of Roussillon (Spain) (or 1014)
- Mufarrij ibn Daghfal ibn al-Jarrah, Jarrahid emir
- Reginar IV, French nobleman (approximate date)
- Chandler, Tertius (1989). Four Thousand Years of Urban Growth. Edwin Mellen Press. ISBN 978-0889462076.CS1 maint: ref=harv (link)
- Palmer, Alan; Palmer, Veronica (1992). Chronology of British History. London: Century Ltd / Barrie & Jenkins. pp. 48–49. ISBN 978-0712656160.CS1 maint: ref=harv (link)
- Rosenberg, Matt T. (2001). "Largest Cities Through History". About.com. Archived from the original on February 18, 2001.CS1 maint: ref=harv (link)