1041 - Harald Hardrada led a campaign against the bulgars

England
The inland city of Worcester in England denied paying naval taxes to King Harthacnut .Edward the Confessor came back from his exile in Normandy to become the heir of his half-brother Harthacnut as King of England. He reduced the fleet from 60 to 32 ships due to the harsh tax burden.
Central Asia
Ingvar the widefarer started an expedition south from Sweden.  Georgian historians mentioned a group of Vikings who helped King Bagrat IV of Georgia in a war against some rebels
Ingvar the widefarer tried to reestablish trade routes to Serkland(Arabia). Ingvar was later killed as his expedition ended in disaster somewhere in central Asia, There are no less than 26 Ingvar related Runestones, 23 of them being in the Lake Mälaren region of Uppland.
Bulgaria
Harald Hardrada led a campaign against the Bulgars.
Italy
March 17: Battle of Olivento was fought near the river Olivento in Apulia. Normans and Lombards led by William Iron Arm was victorious against the Byzantine Empire's Varangian Guard led by Michael Doukeianos, Catepan of Italy, and Harald Hardrada.
May 4: Battle of Montemaggiore fought by the river Ofanto near Cannae in Apulia in the Catepanate of Italy. Normans and Lombards led by William Iron Arm was again victorious against the Byzantine Empire.
Viking trade routes