Glossary of Magic

By Race
Race contributes a significant part to the potential for wielding magical abilities, Elvhen magic was unique and even though there are wide variety of magic types that can be shared among all races, there were few types that humans could never learn. When human first landed in Thedas several thousands of years ago, and fought the elvhen until the the usurping of Arlathan, the best they could do is creating a resembling magic or branch out from the current elvhen magic, not copying it consummately. Beside races, there are diversion come from cultural differences. So city elves - even the ones with pure elven blood - lack the access to Dalish magic and if joined to a circle they will be following the same pattern of humans magic.

Human
Due to having several cultures spread around Thedas, Humans are famous for the wide variety of magic schools.
 * The circle Four schools of magic (Primal - Entropy - Spirit - Creation)
 * Elemental magic
 * Bloodmagic
 * Battlemagic
 * Shapeshifting
 * Sprit healing
 * Death magic
 * Force magic
 * Cleric
 * Seer
 * Illusion
 * Mysticism
 * Summoning
 * Transmutation
 * Shaman
 * Shade
 * Enchanting/Ruin crafting (limited to Tranquils)
 * Artifice

Dalish
Elves in general have better capabilities to learn magic duo to a better connection to "The Beyond" Old elvhen used to have much more powerful magic, but most of it was lost with the destruction of Arlathan. Only small scale of their magic lore is retrieved, but it's still superior to humans in these areas.
 * Advanced form of the Four schools (Primal - Entropy - Spirit - Creation)
 * Keeper magic (Earth and nature)
 * Arcane warriors
 * Shapeshifting
 * Summoning
 * En'an'sal Bora'rahn (Equivalent to Force magic)
 * Ama'Etha Vi (Ostagar's Barrier magic)
 * Vena'vi (Rare school, allows mages to join their magics together)
 * Bloodmagic (Limited, basically for performing the Rite of Vallaslin)
 * Artifice

Dwarves
Dwarves has no connection to the fade and has resistance to Lyrium
 * Only Enchanting
 * High resistance to magic

Kossith
We don't know much about Qunari magic, but Saarebas magic known to be devastating and very destructive. Qunari treat them as dangerous tools to destroy the enemies of the Qun.
 * Elemental (Specifically Electricity) spells is the most common mastery has been witnessed.

By country
Magic training is heavy influenced by the faction where the mages get it. While the strongest structured magical education lies in Tevinter Imperium, there are two other factions that spread world wide and has strong presence in every country:

The Circle of Magi (Loyalists):

The mages who choose to stay under the control of the "white" chantry many limits in studying magic, many schools are forbidden and further experiments within normal schools is not openly done. They maintain the classic training of the four schools (Creation, Spirit, Entropy, and Primal) along with spirit healing being more popular within these circles than anywhere else, also some schools like Transmutation.

The Akademia (Libertarians)

"Freedom" is the key word in Libertarian philosophy, so the order remove most restrictions experiments and teaching of magic, they brought knowledge from Imperial circles and applied it in their Akademia. The typical four schools is taught with great expansion in Primal and Entropy. Battlemagic, and summoning are common as well.

Ferelden
Very rich with many cultures, varied depends on region
 * Libertarians (Kinloch Hold): Typical Libertarians training.
 * Circles of Magi (Denerim/Jainen): Typical Circle training
 * Wilders (The Frostbacks/Korcari Wilds): Shaman, shapshifting, Necromancy
 * Dalish (Ostagar): All Dalish magic listed above

Orlais
The Empire is the seat of the white Divine, so mages lie only in circles under heavy watch of the templars and seekers
 * Typical Circle training + Knight enchanter

Free Marches
Heavy involvement in the war brought all mages factions to the Free Marches.
 * Circles (Kirkwall/Markham/Ostwick): Typical Circle training + Force magic
 * Libertarians (Starkhaven): Typical Libertarians training
 * Resolutionists (Ansburg/War zones): All kinds of magic including forbidden ones, heavy use of Bloodmagic, shapshifting and other dark magic talents
 * Apostates: Depends on the mage's origin

Nevarra
As the home of the dragon hunters, and the great Necropolis in Nevarra has special kinds of magic that rarely seen outside.
 * Death mages (Necropolis): Most advanced Necromancy in Thedas
 * Libertarians (Nevvara city): Typical Libertarian training
 * Circle of magi (Cumberland): Typical Circle training
 * Reavers: Drinking dragon blood in special rituals grant even non-mages some blood magical abilities.

Antiva

 * Circle of magi (Antiva city): Typical Circle training
 * Witches of the Weyrs (Tellari swamps): Necromancy, shapeshifting

Rivain

 * Resolutionists (Nueva Liberatad): As the mages haven, mages train every type of magic in the city, elvhen or human or even Qunari. With the Nueda being famous for their shapeshifting training.
 * Circle of Dairsmuid (Libertarians): Typical libertarians training + Illusion, Mysticism
 * Hedge mages: Xirakè, Seer, Necromancy, Shapeshifting

Tevinter
Left for long centuries with freedom, all kinds of experiments have been done and the Imperium has advanced version of almost every magic Thedas knew, even had stolen some of elvhen magic and developed it in their own way.
 * Imperial Circles: Common Four schools, Battle magic, advanced Summoning including demons,
 * Magisters (Master and apprentice): Bloodmagic is common, Magisters towers are places for highly specified Elemental magic training
 * Gladiators: Different version of elvhen Arcane warriors.
 * Shades: A special shadows manipulation school, all spies from the organization are trained with

Anderfels
The blighted lands has constant conflict with darkspawns, the circle training have focused on means to help ease the suffering of the people.
 * Circle of Magi: Typical circle training, great focus on healing schools

Waters of Thedas
The mages in the open sea have sought mastering the important elements for seafaring, with all freedom they have, they developed them into special schools that can only be trained in the waters of Thedas
 * Water weaving
 * Wind talking