Enchanter: Element of Air. Enchantment is the magic of illusions and charms, of beguiling the mind. Enchanters also specialize in any spells involving air and gases.
Thaumaturgist: Element of Earth. Thaumaturgist deal with spells of a physical and earthly nature, healing, mending and spells dealing with the ground and earth itself.
Pyromancer: Element of Fire. Pyromancy is the magic of fire, light and energy. Usually spells of a destructive nature, pyromancers channel fire and light.
Conjurer: Element of Spirit. Spirit is animus, the element of life. Conjurers deal with spells that summon beings both magical and mundane. They also use spells that directly affect the spirit or soul of a living creature. While conjurors conjure animals and spirits, they are most known/feared for conjuring demons.
Runic Wizardry: Runic wizards are not associated with any particular element, but rather they work through runes and symbols inscribed upon things to channel the forces of the elements, thus they are neutral in their ability with respect to all elemental spells (no specialization bonuses), but by channeling these spells through runes they may gain great benefits. (See Rune Spell)
Necromancy: Necromancy is the only exception to the rule allowing a wizard to specialize in only one element. Necromancy is a hybridization (some say abomination) of Conjury and Thaumaturgy. It combines Earth Magic and Spirit Magic to do vile and unspeakable things, such as animate the dead, control and converse with undead creatures and even occasionally do what only priests can do, bring the dead back to life (this is only done rarely, since it usually is contradictory to the nature of the Necromancer, unless he/she intends to try and enslave the one brought back).