Books with [?] are just guesses. Also, unidentified possible textbooks and required readings are listed below.
Compulsory Classes:
History of Magic
Taught by: Professor Binns, (Florean Fortescue - year 3?)
Textbook:
- A History of Magic by Bathilda Bagshot
Herbology
Taught by: Professor Sprout
Textbook:
- One Thousand Magical Herbs and Fungi by Phyllida Spore
Transfiguration
Taught by: Professor McGonagall
Textbooks:
- A Beginner's Guide to Transfiguration by Emeric Switch (Years 1 & 2)
- Intermediate Transfiguration
Potions
Taught by: Professor Severus Snape
Textbook:
- Magical Drafts and Potions by Arsenius Jigger
Charms
Taught by: Professor Flitwick
Textbooks:
- The Standard Book of Spells (Grades 1 to 4) by Miranda Goshawk
Defense Against the Dark Arts
Taught by: Professors Quirrell, Gilderoy Lockheart, Remus J. Lupin and Alastor "Mad-Eye" Moody
Textbooks:
- The Dark Forces: A Guide to Self-Protection by Quentin Trimble
- Break with a Banshee, Gadding with Ghouls, Holidays with Hags, Travels with Trolls, Voyages with Vampires, Wanderings with Werewolves, Year with the Yeti by Gilderoy Lockheart
Astronomy
Taught by: Professor Sinistra
Textbooks: ?
First Year: Flying Lessons
Taught by: Madam Hooch
Specialization Classes
(You get to choose additional classes for year 3 and higher. Basically, choosing your major or specializing in magic-related fields.)
Arithmancy
Taught by: Professor Vector
Textbook:
- Numerology and Gramatica [?] (Ron borrowed it though and he isn't taking arithmancy)
Divination
Taught by: Professor Sybill Trelawney
Textbook:
- Unfogging the Future by Cassandra Vablatsky
Care of Magical Creatures
Taught by: Professor Kettleburn, Rubeus Hagrid
Textbook:
- The Monster Book of Monsters
Study of Ancient Runes
Taught by: ?
Textbook: ?
Muggle Studies
Taught by: ?
Textbook:
- Home Life and Social Habits of British Muggles [?]
Uncertain Booklist:
Textbooks or Related Class readings that I haven't figured out is for which class:
- Magical Theory by Adalbert Waffling
- Fantastic Beasts and Where to Find Them by Newt Scamander
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