"Ve have just four floors, and the fires are lit only for magical purposes. But ve have grounds larger even than these - though in vinter, ve have very little daylight, so ve are not enjoying them. But in summer ve are flying every day, over the lakes and the mountains -"
-- Viktor Krum describing Durmstrang Institute to Hermione Granger at the Yule Ball (GF23)
Headmasters: Nerida Vulchanova (founder), Harfang Munter, Igor Karkaroff (until fleeing in 1995)
Location: a castle in northern Europe, far enough north that days are very short in winter
Uniform: furs, blood-red robes
Durmstrang Institute was founded by Nerida Vulchanova of Bulgaria, a powerful witch, but whose death was "mysterious". The new head of Durmstrang following her demise was Harfang Munter, who focused teaching on duels and combat/military magic and established the school's reputation for the Dark Arts (Pm).
The Durmstrang Institute building is a castle, not as tall as Hogwarts, having only four floors, but having a larger student population (Pm). Its fires are only lit for magical purposes, or so Viktor Krum claimed. The grounds are quite extensive and include lakes and mountains (GF23).
Durmstrang Institute's location is a well-kept secret, although thought likely to be in the far North of Europe - possibly either charmed to look like ruins or carrying a Muggle-repelling charm. It will also be unplottable so that other wizards will be unable to find it (GF11, GF23). Visitors to Durmstrang are required to submit to memory modifying charms so they cannot reveal its location (Pm). The Durmstrang students travelled to the Triwizard Tournament in an enchanted ship, which helped to mask their starting location (GF15).
Another head of Durmstrang with a dark (and unpopular) reputation was ex-Death Eater Igor Karkaroff. During his Headmastership (c. early 1990s), it was rumoured that Durmstrang did not admit Muggle-born students (GF11). Fearing retribution, Karkaroff disappeared after the return of Voldemort at the end of Triwizard Tournament at Hogwarts (GF35).
- the evil wizard Gellert Grindelwald (DH18) - he carved "his" symbol (actually the symbol representing the Deathly Hallows) into one of the walls, where it remains today (DH8)
- the Bulgarian Quidditch player Viktor Krum (GF15, Pm)
- Poliakoff, a messy boy who came to the Triwizard Tournament (GF16).
Other notes and interesting facts:
- Lucius Malfoy wanted to send Draco to Durmstrang so he could actually learn Dark Arts instead of merely defense against them, but mother Narcissa thought the school was too far away (GF11).
- Even though Durmstrang always had a reputation for encouraging interest in the Dark Arts, student Gellert Grindelwald went too far with his "twisted pursuits" and was expelled. He ended up at the home of his aunt, Bathilda Bagshot, in Godric's Hollow, and befriended young Albus Dumbledore who had just lost his mother and was at home caring for his disabled sister, Ariana (DH18).
- Krum despised Grindelwald and associated him with the symbol of the Deathly Hallows. He and his friends had family members who had been killed by Grindelwald during the war (DH8).
The film implies that Durmstrang is an all-boys school, but that is not canon. In fact, it was founded by a woman (Pm).
Draco was convinced that Durmstrang did not admit Half-Bloods and Muggle-borns, unlike Hogwarts, but that is not confirmed by the canon.
Inconsistency: In one interview, J.K. Rowling was quoted as saying Durmstrang was located "in northern Scandinavia - the very north of Sweden or Norway" ("Jo in Glasgow" December 9, 2000). But this information was not included in her Pottermore entry (Pm). The founder, Nerida Vulchanova, was Bulgarian, as was famous quidditch star Viktor Krum, while Igor Karkaroff's name sounds totally Russian. Gellert Grindelwald's name seems associated with a town in Switzerland, and of course according to Dumbledore's Chocolate Frog Card, he was the "demon" who caused World War II in Germany.
"Although believed to be situated in the far north of Europe, Durmstrang is one of the most secretive of all schools about its whereabouts, so nobody can be quite certain. Visitors ...must comply with memory charms to erase their knowledge of how they got there...." (Pm)
It's possible the author used a memory charm on herself to forget that previous interview.
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).