Classes at Hogwarts

Astronomy
The study of the stars and planets.

Charms
General-purpose incantations and spells with no obvious offensive use (though wards and such may be included)

Defence Against the Dark Arts
Spells and curses for offensive use, mostly for the sake of being able to defend yourself against them. May also include introduction to hostile magical creatures.

Herbology
Study of plants and herbs and how to take care of them properly.

History of Magic
The study of the history of magical society and the developments that led to the world as it is today.

Potions
Study of the use of plants, herbs and other ingredients to make potions with various effects.

Tranfiguration
Spells specifically directed towards changing the properties of objects, both alive and dead.

Ancient Runes
Study of the runic languages and texts written in them. May also include a study of the magical properties of runes.

Arithmancy
Study of numerology, what numbers and math can tell us about the future. May include links to divination and astronomy.

Care of Magical Creatures
Study of the wide range of magical creatures that inhabit the world, how to deal with those that are dangerous, and how to take care of those that can be domesticated.

Divination
Study of various methods of fortune-telling and predicting the future, specifically through use of the instinct and potential of the wizard (as opposed to Arithmancy).

Magical Language & Culture
A study of various languages that are exclusive to the magical world. Elvish, troll, mer, gobbledygook. In the NEWT phase students focus on one language.

Muggle Studies
As the name says, combines study of muggle culture, society and history.