Sesshomaru is Inuyasha's full demon half-brother, who is bent on destroying his sibling and taking away the powerful sword, Tetsuaiga, for his own use.
But there's one problem...
Since Sesshomaru is a full demon, he cannot wield the sword, but pursues it nonetheless.
Sessho sees Inuyasha as weak, because of his human, and emotional side, and also the way he shows care for his friends, and shows absolutely no compassion towards him, half-brother or not.
Sesshomaru is very powerful, and can, at will, transform into an enormous, and very... pouffy white dog-wolf creature.
Tetsuaiga or not, Sessho is very agile, swift, and strong, and a match for Inuyasha everytime they fight.
With Sesshomaru travels a nasty little lackey creature called Jaten, though his loyalty hardly stops Sessho from being willing to sacrifice him whenever an opportunity presents itself.
After one battle, Inuyasha manages to sever one of Sesshomaru's arms, which leads to a union between Sesshomaru, and the powerful enigma which is Naraku- Naraku replaces Sessho's arm with that of a human, though it is not just an ordinary limb, within it is contained a shard of the Shikon Jewel, which enables Sessho to wield the Tetsuaiga.
However this plan fails, as many others, but Sesshomaru never gives up his persecution of Inuyasha and pursual of the sword Tetsuaiga!