Beginner's classes are come-one-and-all affairs, headed up by a kindly old ogre, referred to as 'Professor Of Finding Something And Then Hitting It'. His formal classes usually have a theme, such as "Hittin' Something What Won't Stay Still", or "Movin' Outta Der Way", but mostly you go to the Yard, put your name down, and get matched up with other people. If Old Snagtooth has a knack though, it's pairing up students that can learn a lot from fighting each other.
The Intermediate Teacher is an elf with a number of facial scars, who teaches ranged combat and fencing, and some anatomy of usual combatants. He's constantly trying to improve his own skills, and for a small fee he'll go one-on-one with students and critique their abilities. Just don't ask him about his scars, and you'll be fine.
The Advanced Teacher is a walking arsenal. Word is he's from a far-off exotic land, and that he never leaves his room without fifteen different weapons on his person, and never sleeps without at least five. He keeps his face covered all the time. Occasionally, him and the Intermediate Teacher vanish for a day or two, and return with the Intermediate Teacher nursing a fresh scar on his face. In addition to straight up combat training, he also teaches strategy and tactics for small skirmishes. Oddly, he's never beaten the Beginner teacher at chess.