[1] His parents were Gissur Teitsson and Þórdís Þóroddsdóttir.
After studying in Herford in Germany, he was made bishop of Iceland in 1056 by Athelbjart, archbishop of Bremen.
He built up a see in his family homestead in Skálholt and founded a school.
One of his students was Jón Ögmundarson (1052-1121), who later became the first bishop in Hólar.
His wife was Dalla Þorvaldsdóttir and they had three sons: Þorvaldur, Teitur and Gissur, the latter taking over as bishop after his father's death in 1080.