What is the job of a Hogwarts Headmaster/Headmistress?

Question

As I understand, after Prof. Dippet retired it was the transfiguaration teacher Prof. Dumbledore who became Headmaster of Hogwarts. During the course of the Harry Potter books we see that Prof. McGonagall is the deputy headmistress and the transfiguration teacher. This would mean that Prof. Dumbledore now doesn't hold that teaching position anymore.

So what exactly does a Hogwarts Headmaster/Headmistress do?

Naturally they would appoint teachers and have some amount of administration work including the sending out of letters of acceptance to Hogwarts but what (if anything) else? Don't they have to teach?

EDIT : I get that Dumbledore had many duties being chief Warlock of the Wizemgamot etc., but is there any evidence that all previous Heads had similar duties? I was asking about a Head of Hogwarts in general, not just Dumbledore.

Answer 1

Not very much different from a Muggle school Headmaster:

• Appointing and dismissing teachers and other staff
• Supervision of daily school routine, or delegating this to other staff members: Filch, Hagrid, house elves, etc.
• Supervision of curriculum (with cooperation of the Ministry and Governors)
• Resolving various in-school conflicts as the final arbiter
• Resolving situations that may endanger the school as a whole, not always involving Dark Magic and lethal danger to the world (eg. a threat to shut down Hogwarts, or some Ministry-inspired troubles)
• Sending welcome letters to potential students
• Making speeches at feasts and other special occasions.
• Giving advice to students in difficult situations (not only the Chosen One).

In Muggle schools, the Headmaster is not always an active teacher, sometimes they do have hours in the curriculum, sometimes they don't.