Inuyasha is a half-breed that is part Dog demon and part human. In the original anime called Inu-Yasha, he is fighting Naruku and well... trying to live a normal life. XD
In Elyasia, Naruku is gone and Kagome is back in her own time. Inuyasha was sent to check on his nephew, only to find Mathias wondering off and follow him into a weird realm. Once in the realm of Elyasia, he lost sight of Mathias only to meet Heei. Soon after meeting the fire demon, he got into a fight with him. After a few minutes, Mira who happened to be near by, glared and asked Sinta to stop the two. Once Sinta stopped the fight, Mira went over and looked over both Heei and Inuyasha.
Blah. Go read chapter 06 of part one.
Inuyasha is mated to Nya, who is a fox demon and has a son named Allen who looks just like him.