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Whatever Harry may think at first, Hogwarts is far from being the only wizarding school in the world. However as there are far fewer wizards and witches in the world than there are Muggles, generally there seem to only be one or two schools in each country. Hogwarts is the only school in Britain, and the fact that the Triwizard Tournament is held between only three schools, it seems that these might be the only three in Europe, or at least the three in closest proximity (southeastern Europe isn't represented at the event).
In Britain, at least, wizarding schooling is limited to just seven years. Wizards start much later than Muggles (at age eleven, rather than usually five or six) and do not have to attend Muggle schools prior to their eleventh birthdays (Sch1). There are also no wizarding universities (Sch1), though for some professions, like becoming an Auror, additional job training is required after graduation (OP29).
Headmistress: Olympe Maxime
Uniforms: robes of fine silk; attendants of the carriage wear pale blue
Coat of Arms: two crossed golden wands on a powder-blue field, each emitting three stars
The Academy's building is called the Palace of Beauxbatons, and unlike Hogwarts Castle it does not contain suits of armour. Rather than a Great Hall as at Hogwarts, the Palace contains a Dining Chamber, which is elaborately decorated at Christmastime but in a different style than that used at Hogwarts (GF23). The scholastic system at the Academy is also arranged differently than that at Hogwarts; instead of sitting Ordinary Wizarding Levels or their equivalent at the end of five years, Academy students sit exams after six years (HBP5).
Where is Beauxbatons?
During the feast celebrating the arrival of the students for the Triwizard Tournament, Rowling chose to serve "bouillabaisse". This is a very typical fish soup from the southeast of France and is not really eaten elsewhere, at least not as a common dish. It is likely, then (though an assumption) that Beauxbatons is on the Mediterranean coast of France (maybe by Marseilles) which could explain as well why the students of Beauxbatons are so cold in Hogwarts. -- thanks to Amyll.
The word(s) Beauxbatons, roughly translated from French, means "beautiful wands." In the film, it is implied that Beauxbatons is an all-girls school, but this is not canon.
The Durmstrang Intitute also has a castle, but it is not as big as Hogwarts, having only four floors. Its fires are only lit for magical purposes. The grounds are quite extensive and include lakes and mountains (GF23).
Durmstrang has the reputation of teaching Dark Arts, and it does not admit Muggle-born students (GF11). Gellert Grindelwald was a student here once, and he carved "his" symbol - actually the symbol representing the Deathly Hallows - into one of the walls, where it remains today (DH8).
For more information see the essay, Languages at Durmstrang.
The name Durmstrang comes from the German phrase "Sturm und Drang" which translates to "Storm and Stress." The phrase refers to a movement in German literature in the late 1700s which emphasized "subjectivity and the unease of man in contemporary society" ( The Columbia Encyclopedia). In the film, it is implied that Durmstrang is an all-boys school, but this is not canon.
For more information on Hogwarts, click here.
There are four that we know of: