Well I already said Enchantment Manipulation would be linked to the elemental. Summoning I think that could replace familiar as it sounds much better. Illusions I think has been said already but yeah that'd be good.
Abjuration - Spells that protect, block, banish.
Conjuration - Spells that bring creatures or materials to the caster. Basically summoning.
Divination - Spells that reveal information.
Enchantment - Imbuing items with magic properties.
Evocation - Your run of the mill spells that burn, electrocute, explode, etc.
Necromancy - People know what this is.
Transmutation - Transforming things.
Illusion - Spells that alter perception or create false images. My personal fav.
Ah erm what's the word for healing? I figure Necromancy could be a sub category.
Elemental (This is the idea of drawing, creating and controlling the natural energies these are Level 1 Fire, Water, Wind, Earth, Level 2 (you need two of a previous form to create these) Ice, Lightning, light, Darkness, wood etc Level 3 (the absolute ultimate level) Spirit*, Dimension, Time etc)
Apothecary (The art of potion making.)
Transformation (More details later)
Familiar (This involves creating or enchanting an animal or creature at the basic level this would involve getting close to the animal making it possible for it to communicate (mentally or vocally) at the higher levels this would involve transforming it to fit your needs.
I know Apothecary isn't technically magic in the common sense but it is a practised art.