The Great Dog Demon
A powerful yokai lord who controlled the Western Lands and commanded respect across Japan. He's never actually given a proper name in the series, which is pretty typical for how the story treats older, more significant demons.
He had two sons with different mothers: Sesshomaru, whose mother was a dog demon, and InuYasha, whose mother was human. The manga leaves InuYasha's mother unnamed, though the third movie calls her Izayoi. InuYasha first learns about his father in chapter 12, described simply as "a demon dog that prowled the lands of the west."
His most significant conflict was against the dragon Ryuukotsusei. The Great Dog Demon couldn't outright kill the dragon, but he managed to seal it to a cliff face using his claws—a feat impressive enough that Myouga later points to this battle as what ultimately caused his death. It's one of the few concrete details fans get about what this otherwise distant figure actually accomplished.
Content compiled by AnimeList.moe from publicly available sources.