From The Heretic Knowledge Vault
Generically, one who casts spells. The term is usually restricted to mean those who habitually or professionally use spells as their primary means of winning friends and influencing or incinerating people, from a secular perspective rather than as part of a religious practice. For example, priests in the Veracian Church aren't usually described as mages. Similarly, those who use magic as part of a broader profession (the elven rangers and Viradior, monks in the Ensigerum) are generally described by the profession they practice rather than as mages.
Sources of mages
Not all of the places where one can study to become a mage have been identified yet. The big-name mage school in Tsuiraku is the Sashi Mu Academy of Thaumaturgy and Conjuration, where Meji Hinadori is a student. However, it's doubtful that the mages of Veracia (which is known to have at least some non-Church mages) were educated at Sashi Mu, and we don't know where they come from. The few mages in and around Santuariel appear to be educated through folk knowledge handed down from practitioner to student, as Maxwel did for Ian Samael. The elves apparently don't have to "learn" to use magic; it just ... happens.
Subclasses of mage
The following types of mage have been identified in the story to date:
In the sequence where the Anilis-possessed Ian Samael blasts the headquarters of the Veracian Church, the Veracians mention the existence of "Tsuiraku arch mages". It isn't clear whether arch mage is a subclass of mage or just an honorific given mages of particular power, but they sound nasty, anyway.
There are probably others.