Hogwarts subjects

Charms

The art of moving and manipulating objects by means of waving one's wand and saying magic words. This class is one of the noisier ones; a group of students practicing how to make objects move towards them or how to cause people to laugh makes a lot of hubbub even when they're doing well, never mind when they misfire a lot. Charms is taught from the first year to the seventh.

Filius Flitwick is the current Charms teacher. J. K. Rowling says if she were to teach at Hogwarts, she would teach Charms.

Potions

The art of creating potions with magical effects. The process is delicate and instructions must be followed exactly in order to achieve the desired result. Potions is taught from the first year to the seventh.

Severus Snape is the current Potions master, although he covets the Defence Against the Dark Arts job. Though an exceptional teacher, he is not the fairest disciplinarian, taking pleasure in humiliating students such as Neville Longbottom (for his incompetence in potion-making) and Harry Potter (for personal reasons regarding Potter's father) at every opportunity he gets. Students of his house often like his classes, while those of other houses end up intimidated and/or angry.

Astronomy

Very similar to its real-world equivalent. Astronomy classes take place in the tallest tower and occur every Wednesday. Astronomy is taught from the first year to the seventh. By their fifth year, students are expected to be able to make a star chart.

Professor Sinistra is the current Astronomy teacher.

Flying

The use of enchanted broomsticks. Flying lessons are presumably only given to first-year students.

Madam Hooch is currently teaching flight.

History of Magic

The study of magical history. History of Magic is taught from the first year to the seventh.

The current History of Magic teacher, Professor Binns, isn't very effective. He is the only ghost teacher, extremely set in his ways; some say he didn't even notice he was dead, he just got up one day in the staff room, leaving his body behind.

Binns spends his class drawling on and on, and does not seem to mind (or notice) that the class is never paying any attention.

Herbology

The study of magical plants (such as mandrakess), and how to take care of, utilize and/or combat them. Herbology is set in greenhouses on the grounds. First Years only work in Greenhouse One, as Greenhouse Three contains more dangerous plants. Classes start using Greenhouse Three in their second year.

Professor Sprout is the current Herbology teacher.

Arithmancy

A branch of magic that's concerned with the magical properties of numbers. This class is not taken by Harry Potter, nor by Ron Weasley. It is however the favourite subject of Hermione Granger. Lessons on the subject are not shown and their precise contents remain unknown. The only information given is that the subject is quite hard — therefore attractive to Hermione — and running parallel to Divination lessons at Hogwarts. An optional subject, taught from the third year to the seventh.

Professor Vector is the current Arithmancy teacher and has yet to have a speaking part.

Study of Ancient Runes

Self-explanatory. No details are known, for the same reasons as Arithmancy.

Divination

Predicting the future. Various methods are involved, including crystal balls, palmistry, tea leaves and the interpretation of dreams.

The supporters of the subject claim that it's a fairly inexact science that needs innate gifts more than bookwormish tendencies. Those opposed to the subject claim that it's a load of poppycock and that the teacher is nothing but an old fraud. The latter kind includes Minerva McGonagall and Hermione Granger. Professor Dumbledore even considered dropping Divination from the curriculum altogether, but that changed when he interviewed Sibyll Trelawney. An optional subject, taught from the third year to the seventh.

The current Divination teacher is Sibyll Trelawney. When Dolores Umbridge fired her, she was replaced (to Umbridge's fury) with Firenze the centaur. According to Ginny Weasley, Trelawney and Firenze will be teaching the class together in 6th year.

Care of Magical Creatures

Learning about and to care for magical beasts. Classes are held outside the castle. An optional subject, taught from the third year to the seventh.

At the end of the 1993 school year, the Care of Magical Creatures teacher, Professor Kettleburn, quit because he wanted to enjoy some time with his remaining limbs. As groundskeeper Hagrid had been cleared of opening the Chamber of Secrets, Dumbledore gave him the Care of Magical Creatures job. When he is gone he is replaced by Wilhelmina Grubbly-Plank. Hagrid is rather inexperienced but learning fast; his main problem is an inability to grasp the concept of "terribly dangerous monster".

Muggle Studies

The study of muggles, non-magical people, which involves writing essays such as Why Muggles Need Electricity. Muggle Studies is considered a soft option, but Percy Weasley thinks it is important for a wizard to have an understanding of the non-magical community, especially if he works closely with them. Hermione Granger tried it, but stopped in the third year when she found her schedule too demanding. An optional subject, taught from the third year to the seventh.

Occlumency

The art of shielding the mind against external penetration. Definitely not a part of the usual curriculum.
In Harry's fifth year, Dumbledore arranged for Harry to take one-on-one occlumency lessons with Professor Snape, though Snape told his students that Harry was taking remedial Potions lessons.