Below are the classes you can take in Pokémon Battle Academy. Mandatory ones are marked with an asterisk. Don't take these two seriously, most of them are more for the occasional topic and for a background on your character's preferences.
Biology - Learn about Pokémon at a scientific level. Know how they function, their organ systems, and their habitats.
Breeding - Know how to breed Pokémon to produce the perfect result, with top notch statistics and egg moves.
Coordinating - Bring out the grace and beauty of your Pokémon so that they may compete in contests.
Culinary Training - Learn how to make Poffins, Pokéblock, and more for your Pokémon!
Discovery - Want to know how to find every Pokémon and complete the Pokédex? Learn how in this class.
Gym Leading - Learn how to manage a Gym so that you may run one of your own!
History* - Learn the history of the world and how everything came to be as it is today.
Items - Learn about different items and their effects, so that you may be able to utilize them in battle.
Legends - Learn about the legendary Pokémon and the myths behind them.
League - Learn the inner workings of the Pokémon League. Learn its history, the many jobs you can do, and how to judge Pokémon matches officially.
Moveset - Learn each move known to man and what they do
Music - Learn how to coincide with your Pokémon to play beautiful music together.
Nursing - Learn how to nurse Pokémon like Nurse Joy, so that you may succeed one, as they have to retire eventually.
Photography - Pokémon photography is difficult. Learn how to lure Pokémon and get the best shots!
Pokéatheltics - Learn how to train your Pokémon to both compete beside you and alone in the competition of Pokéathelons.
Pokéconomics - Run a business using the skills taught here. Learn what items are worth, learn about the economy of different regions, and get the skills to work in the towers of Castelia City.
Pokémon Theatre - Learn how to train your Pokémon in theatre, so that they may perform in Unova.
Rangering - Learn how to be a Pokémon Ranger, saving Pokémon and people alike with specialized tools.
Sparring* - Battle your Pokémon against another trainer's. Every class, 6 trainers will be picked at random for 3 battles, so be prepared.
Strategy* - Learn how to utilize strengths and weaknesses in certain Pokémon with strategy, so that you may succeed in battle.