There are four core classes at the academy- Spells, Charms, Potions, and Defense Against Dark Arts.
Every student is required to take them.
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
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