Amlaíb mac Sitric (c. 900–981; Old Norse: Óláfr Sigtryggsson), commonly called Amlaíb Cuarán, in Old Norse: Óláfr kváran, is a 10th-century Norse-Gael who is King of Northumbria and Dublin.
His byname, cuarán, is usually translated as "sandal".
His name appears in a variety of anglicized forms, including Olaf Cuaran and Olaf Sihtricson, particularly in relation to his short-lived rule in York.
He is the last of the Uí Ímair to play a major part in the politics of the British Isles.
Amlaíb is twice, perhaps three times, ruler of Northumbria and twice ruler of Dublin and its dependencies.
His reign over these territories spans some forty years.
He is a renowned warrior and a ruthless pillager of churches, but ends his days in retirement at Iona Abbey.
Born when the Uí Ímair rule over large areas of the British Isles, by his death the kingdom of Dublin is a minor power in Irish politics.
At the same time, Dublin becomes a major center of trade in Atlantic Europe and mastery over the city and its wealth becoms the supreme prize for ambitious Irish kings.
In death, Amlaíb will become the prototype for the Middle English romance character Havelok the Dane.
In life he is a patron of Irish poets and Scandinavian skalds who write verses praising their paymaster.
Amlaíb is married at least twice, and has many children who marriy into Irish and Scandinavian royal families.
His descendants are kings in the Isle of Man and the Hebrides until the 13th century.
