Takamichi T. Takahata is the art teacher at Mahora Academy—the position Negi takes over later in the series. He's a former member of Ala Rubra, the legendary magical group that fought in a major war; despite being just a kid back then, he was already an active combatant. He's well-known and respected in magic circles, though he never formally graduated from magic school because he can't cast spells the traditional way.
Instead, Takahata developed his own fighting style called kankahō, which blends eastern Ki techniques, western magic, and iaiken—basically iaidō but bare-fisted. It's a pretty unique approach, and fans often note that both his combat style and his whole demeanor (including his smoking habit) were heavily inspired by Gateau von Vandenberg, his master and fellow Ala Rubra member.
The complicated part: Asuna is completely fixated on him, but Takahata keeps major secrets from her. He erased her memories of the Magic World, and he's openly said he doesn't deserve to be loved—though the exact reason remains unclear. There's clearly a lot of baggage there.
Content compiled by AnimeList.moe from publicly available sources.