Arcane -

Wizard/Mage

Someone who acquired their magic through knowledge and practice

Faith -

Cleric/Druid

Someone who gained magic through god or other similar entity

Devotion -

Occultist/Witch

Someone who obtained magic through a pact or deal with a dark force

Pyromancy -

The manipulation and creation of fire/heat

Geomancy -

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The manipulation of earth and metal

Hydromancy -

The manipulation and creation of water and ice

Aeromancy -

The manipulation of air and creation of lightning

Necromancy -

The manipulation of corpses and souls

Chronomancy -

The manipulation of time

(Warning: Very dangerous, could cause time loop or timeline distortion)

Alteration -

The use of magic to manipulate how physical and magical forces interact

Illusion -

Creating non physical constructs or changing the way people perceive things

Restoration -

The use of magic to heal and in rare cases resurrect living things

Conjuration -

Transportation of people, creatures and objects

Enchanting -

Applying magic to physical items that can typically be used many times

Alchemy -

Mixing magical and non magical substances to create something with an empowered effect or a new effect

Golemancy -

The use of Enchanting and sometimes Alchemy to create constructs

Divination -

A gift or curse from a god that allows the user to look into the future with varying amounts of accuracy