Mages use their extensive knowledge and lore of magicka in every way which will help them to solve any given problem. Though most Mages tend to specialize into one school of magic it is not uncommon for a Mage to have significant skill in all schools of magic including the art of alchemy.

Schools of Magic:
�•Destruction
�•Alteration
�•Restoration
�•Illusion
�•Mysticism
�•Conjuration
�Enchanting

http://elderscrolls.wikia.com/wiki/Mage_(Class)