Appearance and personality
Asgeir is a man of average build, with long hair, a moustache and a braided beard. His weapon of choice appears to be a sword, although he is often seen carrying a dagger on his belt as well. Asgeir seems to be very intelligent and is oftentimes seen giving advice to and watching over Thorkellー or being in charge of battle strategics (as seen in the 'Baltic Sea War' arc).
He was first introduced to the story in chapter 21 when briefly interacting with Thorkell, followed by a few similarly minor background appearances. Asgeir is spotlighted for the first time when interfering in the fight between Thorkell and Thorfinn, threatening to kill the latter.
Asgeir and other characters
Asgeir appears to have a very close bond with Thorkell. He is one of the few characters Thorkell seeks to meet at eyelevel in conversation, listens to Asgeir's advice and puts him in charge of strategics and planning (as seen in the Baltic Sea War chapters onward). Although Asgeir breaks up the duel of Thorfinn and Thorkell and thereby dishonours Thorkell, he appears to accept Asgeirs commands (although reluctantly) which shows a great level of respect on Thorkells side. Asgeir seems to reciprocrate this feeling of respect as he adresses him with his rank 'Boss/Captain' (jp. 大将, taishô) instead of his first name in public. From Thorkell's second fight with Thorfinn it also becomes clear that he puts his Captain's life over the important viking concept of 'Warriors Pride', which is quite unusual and hints at a certain depth of Asgeir and Thorkell's bond. He appears to know his boss very well and does not seem to be afraid of him because Asgeir does not back away even when Thorkell actively attempts to strangle him. The Vinland Saga anime director Shûhei Yabuta remarked that their bond is interesting and unique and that he plans to explore it even further in the anime adaptation.
SigurdAsgeir does not seem to be too fond of Sigurd at first since he makes fun of him by calling him by the wrong name 'Mr Willing' (jp. 元気君, genki kun) on purpose for almost the entirity of the Baltic Sea War arc ー although knowing better and being repeatedly told by Sigurd that he indeed is called Sigurd. It might also be that he teases him because as Thorkell seems to like Sigurd a lot and even gives him weapons to fight alongside him, Asgeir appears not to understand that fondness at first. This might be the reason why he chose the nickname 'Mr Willing' (translation varies) because Thorkell and Sigurd himself keep saying that he is very willing to help. However, Asgeir's rather negative image of Sigurd seems to change after Sigurd is able to trace the hidden entrance to the Jomsburg fortress ー a test he had Sigurd put to, apparently not too optimistic about a successful outcome at first. After Sigurd's success Asgeir appears to have accepted Sigurd and even offers him a boat and the possibility to join Thorkell's band as a reward.