Anund Jakob was the eldest son of Olof I, and the only one born to his 'Christian' wife Estrid. He was the first Svealandic king to be Christian from birth, being baptized with the name Jakob. The Svealandic Thing objected to the non-Norse name however and referred to him as Anund. His other name, Kolbranna seems to a be a reference to his practice of burning down his opponents' houses.
Anund had been made co-king with his father in 1018 after Olof's dealings in Hordaland backfired and it appears he succeeded him smoothly in 1022 when Olof died.
He also helped Stenkil cement his rule over Gothenland and he would be recognised as the country's first king. Anund gave him his niece in marriage. Not much else is known about the king, other than he most probably campaigned with his brother-in-law Yaroslav the Wise in the Kievan Rus'.
It is not even known when he actually died only however it is assumed it was around 1050. He would be succeeded by his half-brother Emund.