There are four core classes at the academy- Spells, Charms, Potions, and Defense Against Dark Arts.
Every student is required to take them.
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Here are the professors for each class:
Spells- Still looking for one to hire!
Charms- Professor Maestra
Potions- Professor Nini
Defense Against Dark Arts- Professor Andra
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Potions Class Page: http://club-penguin-wizard-school.wikia.com/wiki/Potions_Class
Charms Class Page: http://club-penguin-wizard-school.wikia.com/wiki/Charms_Class