I haven't defined exactly how magic will work yet, but I have sketched out a little about how it will be organized.

The official place to learn magic is the University of Magery, which is the dominant institution in the city where it is based (let's call it "Magic City" until I come up something).  The city and the university are seeped in magic, Magic City is a real "college town".  The city, university and most of the key magic artifacts were destroyed by the enemy in the war, so we'll never see them in the present.  They are in the process of rebuilding.

The University of Magery is organized like Cambridge University in England; the University is really just the overarching umbrella for a series of specific colleges of magic.  They are:

The College of Fire
The College of Air
The College of Earth
The College of Water

You get the point, they're all the "College of."  There are 20 in all.  The four above represent the fundamental forces of magic, and are (usually) the most established, prestigious and wealthy colleges.  The other 16 colleges spun off from the first four some time in the past (they are various ages).

The other colleges are:
Metastudies (studies about the nature of magic itself)
Transformation - Organic (transforming organic materials)
Transformation - Inorganic (transforming inorganic materials)
General Studies

Within each college there are all sorts of specialities; you can think of them as majors.  Traditionally, new colleges form when a group of faculty with a particular interest can wrangle enough resources to start a new "official" specialty.

The colleges have varying levels of influence, prestige, wealth and respect.  Typically, the four founding colleges are the most revered, and the younger and more practical a college is the less prestigious it is.  This status of a college is reflected in it's facilities and public perception.  The colleges have varying levels of rivalry and cooperation, and every college tells jokes/makes fun of the other colleges to various degrees.  There are clear stereotypes of the various colleges, some of which are true, and some aren't.

Each college attracts it's own unique characters (in students and faculties) and has it's own unique culture.  Some are progressive and liberal, some are conservative.  Some are relatively accepting of diversity, others aren't (the Old Boy's network is well ensconced in almost of them, however).

There are all sorts of odd inconsistancies in the system.  The College of Food, for instance, isn't glamorous or prestigious, and is often made fun of by the big schools, but it is, in fact, one of the wealthiest schools, because it is their spells that keep the food supply safe, healthy and preserved!

The College of Fire, on the other hand, is the most glamorous and the most cocky, with beautiful looking buildings and flashy members, but actually struggles for funds, because they largely eschew practical applications of their magic.

Flashbacks to the College of Magery will give us insight into key moments in Davis and Axe's histories, and provide a lot of context for the society in general.

I spent a semester at Cambridge University in England, and it is really the inspiration for the College of the Magery.  Basically, the two cities are the same in my mind!

I picture the College of Magery as a generally lighthearted portrayal of higher ed and a true "college town."  I could actually picture a whole fun book series based there.