From the perspective of Muggles, the Harry Potter Verse is no different from our world, but they don't know there is a whole society of wizards hidden by the Masquerade. Why? Well, back in The Middle Ages wizards and Muggles didn't get on so well.
Magic is genetic, but has to be refined through instruction at a Wizarding School. Despite this, magical children are often born of Muggles, although these so-called "Muggle-borns" get to face Fantastic Racism in the wizarding world, complete with the Fantastic Slur "Mudblood". In fact, the disagreement over whether or not Muggles-borns are going to result in the downfall of magic is the main rift in the verse. Those who think they are tend to use Black Magic and make attempts to Take Over the World with designs of creating a new order in which Muggle-borns (to say nothing of actual Muggles) would be massacred and/or enslaved.
The series is set entirely in Great Britain, mainly at the British wizarding school Hogwarts, which is located in a remote part of the Scottish Highlands. According to the official timeline, the books are set in the 1990s, although Rowling seems to have forgotten this a couple times and the movies out-and-out ignore it. The main conflict in the series is the second war against Lord Voldemort and his Death Eaters, the first war having ended when Voldemort tried to kill Harry Potter as a baby and was defeated by The Power of Love. As Harry joins Hogwarts and forms a Power Trio with Ron Weasley and Hermione Granger, Voldemort slowly regains his powers and builds up his forces again to start the war anew.
For most of the series, the elected government of Wizarding Britain--Ministry of Magic--is a conservative and rather eccentric Obstructive Bureaucracy that ends up Dying Like Animals once Voldemort shows up again. In the final book, they even get secretly conquered by Voldemort and staffed with Black Shirts. Kind of like the rest of Britain.
Some of the more prominent non-human races in the series:
- Centaurs: A seemingly One-Gender Race of Isolationist Fortune Tellers, although one centaur, Firenze, says My Species Doth Protest Too Much and helps out the good guys. The other centaurs disown him.
- No females are seen. This does not entirely preclude their existence.
- Giants: Brutes who talk in Hulk Speak and can breed with humans; Hagrid is half-Giant.
- Goblins: All Devouring Black Hole Loan Sharks who are True Neutral. They can breed with humans as Professor Flitwick is known to be part-goblin.
- House-elves: A race of happy slaves which are generally owned by the very wealthy. The house-elves working at Hogwarts are treated humanely by Dumbledore, but others are not so lucky. Hermione forms the Society for the Promotion of Elfish Welfare to try and end their enslavement, but for the most part the elves themselves are very happy with their lot in life.
- Veela: A drop-dead gorgeous race of people with neat powers, whose 'true form' apparently resembles harpies. They can breed with humans, resulting in Fleur Delacour.
- Werewolves: Not actually a race, but they deserve mention here. Lycanthropy is The Virus and is passed on through being bitten. Victims involuntarily transform into a werewolf during the full moon, at which point they become compelled to Kill All Humans. However, they are normal humans (good or evil) the rest of the time, and can breed with them with (apparently) no side-effects. Nevertheless, they are feared even in human form and face a lot of discrimination.
The rules for determining what is canon in this verse basically come down to "if Rowling wrote it or said it, it's canon". The movies take place in an Alternate Continuity and are generally considered to be Word of Dante in regards to the "proper" book canon. The series lacks an Expanded Universe since Rowling exclusively owns the publishing rights.
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