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Tryggvi Ólafsson (died 963,) also Tryggve Olafsson, was the King of Viken (Vingulmark and Ranrike), and the son of Olaf Haraldsson, king of Vestfold, and grandson of Harald Fairhair.

Tryggve ravaged in Ireland and Scotland, and performed Viking cruises in the West sea. In 946 king Haakon went north, and set Trygve over Viken to defend that country against enemies. He gave him also in property all that he could reconquer of the country in Denmark, which the summer before king Haakon had subjected to payment of scat to him.

Tryggve was killed by Eirik Bloodaxe's son Harald Greycloak as part of Harald's effort to reunite all of Norway under his rule.

Tryggve's son, Olaf Tryggvason, later became King of Norway, and his daughter Ingeborg Tryggvasdotter married Ragnvald Ulfsson, the earl of Västergötland and later the ruler of Staraja Ladoga.