Muggles' Guide to Harry Potter/Places/Durmstrang Institute

General Overview
Durmstrang Institute is a wizarding academy, similar to Hogwarts School, believed to be located somewhere in western Russia or northern Europe. When we first hear of it, it is run by headmaster Professor Karkaroff. Durmstrang Institute is traditionally a competitor in the long-dormant Triwizard Tournament against Hogwarts and Beauxbatons Academy of Magic.It does not accept muggle-born witches and wizards.

Extended Description
In Harry Potter and the Goblet of Fire, Draco Malfoy, on the Hogwarts Express, mentions that he could have gone to Durmstrang, and that they actually teach Dark magic there (although use of Dark Magic outside classes is forbidden). Apparently he had been discussing the Triwizard Tournament with his cronies, but we don't find out about the Tournament until a short while later.

The Durmstrang contingent arrive for the Triwizard Tournament in a ship that surfaces in the middle of the lake at Hogwarts. Their headmaster, Igor Karkaroff, hustles them inside the castle because "Viktor" has a cold. Ron is astounded to discover that "Viktor" is the famous Quidditch Seeker, Viktor Krum.

Viktor becomes the Champion for Durmstrang in the Triwizard Tournament. He acquits himself reasonably well, being in the running with Cedric and Harry up until the final Task.

At the Yule Ball, Krum mentions some aspects of Durmstrang school life to his date, Hermione. Karkaroff chides him for revealing Durmstrang's secrets. Professor Dumbledore, in response, suggests that nobody should claim to know all the secrets of any of the schools, mentioning a room he had found once and never again.

Karkaroff is a former Death Eater who reduced his time in Azkaban by selling out his fellow Death Eaters to the Ministry. As such, when Voldemort returns, Karkaroff flees, and nothing is heard of him for slightly over a year. We do not know who becomes headmaster in his absence.

With Karkaroff having fled, Ron worries that, at the end of the school year, the Durmstrang group may be stuck at Hogwarts with nobody to sail their ship back home. Viktor reassures him that there will be no problem; the Headmaster had stayed in his cabin for almost the entire outward trip, leaving the ship handling to the students, so they were well prepared to handle the voyage.

We learn in Harry Potter and the Deathly Hallows that Gellert Grindelwald was educated at Durmstrang. Viktor Krum, when he had been a student there, was disturbed because Grindelwald's symbol, a line within a circle within a triangle, was a fairly frequent piece of graffiti, and because many students claimed to agree with Grindelwald's beliefs about the inherent superiority of Wizards over Muggles.

Analysis
There really is very little basis in the stories for assigning a location to Durmstrang Institute. We do learn that it is a colder land than England, that there are glaciers and mountains there, the student Viktor Krum is Bulgarian, and the headmaster, Karkaroff, has an Eastern European name. Gellert Grindelwald, however, has a German name, and was also a student there. What facts we have, apart from Grindelwald, would seem to indicate Eastern Europe, particularly in the north, or Scandinavia, as possible sites for the school, but Switzerland, particularly the higher altitudes, would also fit the known facts, despite having no outlet to the sea. Whether sea access is necessary for the Durmstrang students' magical ship is uncertain, as we don't believe there is any sea access to the Hogwarts lake. The name being apparently based on German would suggest Switzerland as well, though Russia is equally a possibility, as many Russian cities, such as Saint-Petersburg and Yekaterinburg, have German names. The Kola peninsula near the border with Finland seems somewhat likely as a location. The name Durmstrang was probably derived from Sturm und Drang, German for storm and stress. There is no explanation for a school possibly located in Eastern Europe having a name based on German words; however, the name of the school will have been established by its founders, who might well have been Germans fleeing persecution.

Possibly surprisingly, the revelation that there are Wizarding schools other than Hogwarts comes as something of a surprise to the reader. Once their existence is revealed, however, it becomes obvious that there must be Wizarding schools in other countries; we see nobody at Hogwarts except those who come from the British Isles, there must be some place for European witches and wizards to be educated. Similarly, we must assume the existence of Wizarding schools in North America. The town of Salem, Massachusetts, is mentioned in the series a few times; perhaps this is where the North American wizarding school is located?

It is noted that Durmstrang emphasizes the Dark Arts more, or is believed to. We see no evidence of this in any of the students; possibly this is simply reputation the school has gained from being located in a dour and forbidding land. It is true that Grindelwald, the dark wizard, was educated there; however, it is also true that Voldemort was educated at Hogwarts, and Hogwarts has not gained any similar reputation.