Access to the arcane university is required so that you can use the spell making altars. These altars can be found in the praxographical center. Make the following spells to upgrade the corresponding spell type:
Repeatedly cast the spell you have created by tapping the cast button continuously and you can get all your magic levels up to 100. Note that if you use the fire damage spell, it has to actually hit a target, hopefully a high level monster so that you don't have to stop.