|Ab urbe condita||1788|
|Balinese saka calendar||956–957|
|English Regnal year||N/A|
|Chinese calendar||甲戌年 (Wood Dog)|
3731 or 3671
— to —
乙亥年 (Wood Pig)
3732 or 3672
|- Vikram Samvat||1091–1092|
|- Shaka Samvat||956–957|
|- Kali Yuga||4135–4136|
|Japanese calendar||Chōgen 8|
|Minguo calendar||877 before ROC|
|Seleucid era||1346/1347 AG|
|Thai solar calendar||1577–1578|
1161 or 780 or 8
— to —
1162 or 781 or 9
|Wikimedia Commons has media related to 1035.|
- July – The 8-year-old William I becomes duke of Normandy after his father Robert I (the Magnificent) dies on a pilgrimage at Nicaea (modern Turkey). Robert's death leads to a period of instability in Normandy as William is too young to take his father's place. The Norman nobles in the region take the opportunity to settle old feuds and to increase their private wealth.
- Emperor Conrad II (the Elder) grants the city of Koper (modern Slovenia) with town rights and some degree of self-government within the Holy Roman Empire.
- October 16 – Conrad II grants the right to hold the first Freimarkt festival in Bremen. The city increases her trade with Norway and the northern Netherlands.
- October 18 – King Sancho III of Pamplona dies and divides his dominions among his four sons, García Sánchez III, Gonzalo I, Ferdinand I and Ramiro I.
- Pisa launches a naval assault against the Saracen pirates strongholds in the Lipari Islands.
- November 12 – King Cnut (the Great) dies at Shaftesbury leaving the rule of England in dispute between his sons Harthacnut and Harold Harefoot. The earls of Northumbria and Mercia support Harold's claim while Godwin (Earl of Wessex) supports Harthacnut. Harold is elected as regent or joint ruler of England. Cnut is buried in the Old Minster in Winchester.
- Winter – Harthacnut is unable to travel to his coronation in England because his Danish kingdom is under threat of an invasion by King Magnus I of Norway and King Anund Jacob of Sweden.
- Dharma Pala, Indian ruler of the Pala Dynasty (d. 1060)
- Henry of Burgundy, French nobleman (approximate date)
- Hereward (the Wake), English nobleman (approximate date)
- Hermann of Salm, German nobleman (approximate date)
- Isaac Albalia, Andalusian Jewish astronomer (d. 1094)
- Leofwine Godwinson, English nobleman (approximate date)
- Nathan ben Jehiel, Italian Jewish lexicographer (d. 1106)
- Robert I (the Frisian), count of Flanders (approximate date)
- Urban II, pope of the Catholic Church (approximate date)
- April 13 – Herbert I, French nobleman (approximate date)
- May 26 – Berenguer Ramon I, Spanish nobleman (b. 1005)
- May 30 – Baldwin IV (the Bearded), French nobleman (b. 980)
- October 18 – Sancho III (the Great), king of Pamplona
- November 4 – Jaromír, duke of Bohemia (Přemyslid Dynasty)
- November 12 – Cnut, king of Denmark, Norway and England
- Abu Ali ibn Muhammad, ruler (malik) of the Ghurid Dynasty
- Astrid Olofsdotter, queen consort of Norway (House of Munsö)
- Drogo of Mantes, count of Valois and the Vexin (b. 996)
- Estrid of the Obotrites (or Astrid), queen consort of Sweden
- Guo, Chinese empress and wife of Ren Zong (b. 1012)
- Harun, Ghaznavid governor and ruler (shah) of Khwarazm
- Ibn al-Samh, Moorish astronomer and mathematician (b. 979)
- Richard fitz Gilbert, Norman nobleman (approximate date)
- Robert I (the Magnificent), duke of Normandy (b. 1000)
- Svein Knutsson, king of Norway and son of Cnut (the Great)
- Yahya ibn Ali ibn Hammud al-Mu'tali, Hammudid caliph
- The Gesta Normannorum Ducum of William of Jumièges, Orderic Vitalis, and Robert of Torigni, Ed. & Trans. Elizabeth M.C. van Houts, Vol. I (Clarendon Press, Oxford, 1992), pp. 80-85.
- Benvenuti, Gino (1985). Le Repubbliche Marinare. Amalfi, Pisa, Genova e Venezia. Rome: Newton & Compton Editori. p. 42. ISBN 88-8289-529-7.