Magic is made up from 12 basic affinities each of which combine with one another to form 81 composite affinities when it comes to spell casting at least Mark casting there are eight methods each of which combine to form composite methods.
Each Affinity covers a certain type of magic, while each method covers an application of that magic, when combined these represent the abilities of a character.
The main uses of gems are:
Providing mana and empowering spells.
Allowing people to cast spells outside of their Mark Affinities and Methods
Allowing the effect of a spell to have permeance
Powering patterns and devices
Acting as currency
Because gemstones act as a source of mana, and can empower a spell, they can be used as tools to help in the learning of magic.