A mysterious ayakashi that was sealed in a shrine until he was accidentally released by Natsume Takashi. Since Madara was trapped in a material form for so long, he ordinarily takes on the shape of a maneki neko (lucky cat), leading Natsume to nickname him Nyanko-sensei. In this form, other people can see him.
He is a powerful ayakashi, who protects Natsume from others and teaches him spells on occasion, in return for Natsume's promise to give him the Book of Friends when he dies. As the story progresses, Madara takes a liking to Takashi.

Source:Wikipedia