Kjartan was the son of Olafur pa and Thorgerdur Egilsdottir. He had some brothers and sisters, like Thuridur, Halldor and Steinthor, and one foster-brother, Bolli, who was in fact Kjartan's cousin. Kjartan got married to Hrefna Asgeirsdottir and they had the son Asgeir,
Kjartan was the most handsome man in Iceland. He had a beautiful face and long, blond hair. He was also a big and strong man. Kjartan was dexterious in arms and fought better than any other man.
As the story goes on Kjartan and Bolli become severe enemies. Mostly this is because Kjartan doesn't want to forgive Bolli. Because of this Kjartan and some others must die.
Kjartan had a strong will and sometimes went too far. In fact he was a big ego and never gave anyone else a thought! You could say that he died because of his pride. He was revengeful as can be seen when he didn't want Gudrun and Bolli to buy the farm Tunga and bought it himself only so that they couldn't live there.