Sesshomaru is also called "Fluffy" on rabid fan girl sites. If you called him that in front of him, he'd probably give you a slow and painful death. Anyway, he's Inu-Yasha's half brother, but Sesshomaru, unlike Inu-Yasha, is full demon. He's obsessed with stealing Inu-Yasha's Tetsusaiga [yes, I DID spell that right], not happy with his won sword, Tensusaiga. [not sure about that spelling.] His sword can only save or heal human lives as Inu-Yasha's sword only protects human lives. In a fight with his brother, Inu-Yasha cut off Sesshomaru's left arm clean off. He's thought of as heartless and cold, although he saves Rin's life.
