1041

• December 10 – Emperor Michael IV the Paphlagonian dies after a 6-year reign. His wife, Empress Zoë, elevates (on the advice of her lover John the Orphanotrophos) her adoptive son to the throne of the Byzantine Empire, as Michael V Kalaphates. Shortly after, Michael comes into conflict with his uncle John, and banishes him to a monastery.

• March 17 – Battle of Olivento: Norman troops and their Lombard allies, led by William Iron Arm, are victorious against the Byzantines at the feet of the Monte Vulture, near the River Olivento in Apulia.
• May 4 – Battle of Montemaggiore: Lombard-Norman rebel forces, led by William, are again victorious, and defeat a Byzantine army (18,000 men) on the hill of Montemaggiore, near the River Ofanto.
• September 3 – Battle of Montepeloso: Lombard-Norman rebel forces, led by William, defeat the Byzantines at Montepeloso. During the battle, Boioannes, governor of the Catepanate of Italy, is captured.
• Winter – Battle of Ostrovo: The Byzantines, with the help of the Varangian Guard, led by Harald Hardrada (future king of Norway), defeat the Bulgarian troops, near Lake Ostrovo in Greece.

• King Harthacnut invites his half-brother Edward the Confessor to return to England from exile in Normandy as his heir as king of England,{{cite ODNB|last=Lawson|first= M. K.|id=12252|title=Harthcnut|date=2004-09-23}} with the support of Godwin, Earl of Wessex.Quadripartitus.
• The city of Worcester rebels against the naval taxes of Harthacnut. He reduces the navy from 60 to 32 ships.

• The Zirid dynasty rejects Shi'ite obedience and Fatimid domination, and recognizes the Abbasids as their overlords.Gilbert Meynier (2010). L'Algérie cœur du Maghreb classique. De l'ouverture islamo-arabe au repli (658-1518). Paris: La Découverte; p.50.

• At about this time, the number of enlisted soldiers in the Song dynasty Chinese military reaches well over 1,250,000 troops, an increase since 1022, when there were a million soldiers.

• Ōe no Masafusa, Japanese poet (d. 1111)
• Raymond IV, Count of Toulouse (Raymond of Saint-Gilles), French nobleman (d. 1105) (approximate date)

• February 4 – Fujiwara no Kintō, Japanese poet (b. 966)
• December 10 – Michael IV the Paphlagonian, Byzantine emperor (b. 1010)
• Adolf II of Lotharingia, German nobleman (b. 1002)
• Akazome Emon, Japanese waka poet (approximate date)
• Eadwulf IV of Bamburgh, Northumbrian ruler
• Edmund of Durham (or Eadmund), English bishop
• Gangeyadeva, Indian ruler of the Kalachuris of Tripuri
• Mac Beathaidh mac Ainmire, Irish poet and Chief Ollam
• Muhammad of Ghazni, sultan of the Ghaznavids (b. 998)
• Muhammad ibn Rustam Dushmanziyar, Buyid emir
• Peter Delyan, Bulgarian rebel leader and ruler (tsar)
• Sampiro, Spanish bishop, politician and intellectual
• Tancred of Hauteville, Norman nobleman (b. 980)
• Vikramabahu, Prince of Ruhuna (or Kassapa), ruler of Sri Lanka (b. 1017)

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