Hogwarts School of Witchcraft and Wizardry:

Head: Albus Dumbledore (until his death)
Location: Scotland, U.K.
Castle: Large with over 7 stories and many towers. It has fairly large grounds with a quidditch pitch, a lake, and has the forbidden forest at the edge of the grounds.
Uniform: Black robes. They also have dress robes for special occasions.

Durmstrang Institute:

Head: Igor Karkaroff (until his death)
Location: Probably Bulgaria (seeing that Krum is on the Bulgarian national quidditch team).
Castle: Has 4 floors and is smaller than Hogwarts, however it has more land.
Uniform: Furs and thick clothing (very cold there)
Notes: They attend the Triwizard tournament in Book 4 and their champion is Victor Krum, who comes in 3rd place. It does not admit muggle borns and is very into the dark arts.

Beauxbatons Academy of Magic:

Head: Olympe Maxime
Location: France
Castle: Has ice sculptures around the dining chamber at Christmas with wood nymphs that serenade around the students as they eat.
Uniform: Made of silk that are pale blue
Notes: Their coat of arms has 2 golden wands crossed, each admitting 3 stars.

Salem’s Witches Institute:

An American School that was mentioned in Book 4, as Harry, Ron, and Hermione passed by some American witches.