There are three main schools of magic which magi use: Arcane, Fire and Frost. Certain adversaries can be resistant to a particular school of magic. If you find that a creature is resisting many spells of a certain type, try switching to another school. You can find some examples of each school of magic, below:

Arcane Magic

Arcane Intellect (Buff) - Increases the target's Intellect by X for Y min. Always have this ability active on yourself and cast it on other players that need it as well.

Arcane Brilliance (Party Buff) - Infuses the target's party with brilliance, increasing their Intellect by X for 1 hour. Requires Reagent: Arcane Powder. This is more mana-efficient way of quickly giving all your party members the intellect buff. This spell is only available for level 56+ players via a looted book.

Arcane Missiles - Launches Arcane Missiles at the enemy, causing X damage each second for Y seconds. This spell has a spectacular animation.

Arcane Explosion (AOE) - A powerful area of effect spell which causes an instant explosion of arcane magic around the caster, causing X to Y damage to all targets within Z yards. This ability is useful when the caster is surrounded by targets.

Fire Magic

Fire Blast - Blasts the enemy with fire for X to Y fire damage.

Fireball - Hurls a fiery ball that causes X to Y fire damage and an additional D damage over Z sec.

Flamestrike (AOE) - Calls down a pillar of fire, burning all enemies within the area for X to Y fire damage and an additional Z damage over A sec.

Fire Ward - Absorbs X fire damage. Lasts 30 seconds. Use this ability when facing a fire damaging monster.

Scorch - Scorch the enemy for X to Y fire damage.

Frost Magic

Frostbolt - Launches a bolt of frost at the enemy, causing X to Y frost damage and slowing movement speed for Z sec. This ability is useful for stopping monsters from running away and warning their friends.

Frost Nova - Blasts enemies near the caster for X to Y cold damage and freezes them in place for up to Z sec. This is a main ability for the Mage. It is useful in stopping monsters from chasing you, allowing you to get away. It can also be used in combat to finish off weakened, retreating monsters. Subject to diminishing returns in PvP. This is considered an immobilizing effect.

Frost Armor - Increases armor by X for 30 minutes. If enemies strike the caster, they may have their movement speed slowed to 70% and have their attacks slowed by 20% for 5 seconds.

Blizzard (AOE) - Ice shards pelt the target area doing X damage over 8 seconds.

Cone of Cold - Targets in a cone in front of the caster take X to Y frost damage and are slowed to 50% of normal speed for 8 seconds. This spell can be improved through a talent.

Frost Ward - Absorbs X frost damage. Lasts 30 seconds.

This page does not have a complete listing of all abilities that are available.

Polymorph - Polymorph transforms enemy Beasts, Humanoids, and Critters into a sheep, forcing it to wander around for the duration of the spell. While wandering, the sheep cannot attack or cast spells and will regenerate health very quickly. Only one target can be Polymorphed at a time and any damage will transform the target back into its normal form. Players targets have a decreased duration of the effect and a better chance to break free. Multiple castings on a single target are subject to diminishing returns for the spells' durations.

Blink - Teleports the caster to the targeted location, breaking free of any bonds that hold the Mage. One of the mages key abilities, it has multiple uses, from escaping a monster's spell or physical attack, to traveling.

Mana Shield - Absorbs X physical damage, draining mana instead. Lasts 1 minute. This is a useful ability which can buy the caster enough time to escape or deal the final damage needed to defeat an enemy. This ability can be improved through a talent.

Counterspell - Counters the enemy's spell preventing him from casting any spell from that school of magic for 10 sec. This spell can be improved through a talent so that it also silences a target and prevents him from casting any spells for 4 seconds.

Remove Lesser Curse - Removes 1 lesser curse from a friendly target. This is an especially useful ability.

Portal - Creates a portal, teleporting group members that use it to X. You need to go get training for specific locations. This ability requires a reagent to use. Each portal spell has an individual cooldown.

Teleport - Teleports the caster to X. You need to go get training for specific locations. This ability requires a reagent to use.

Dampen Magic - Dampen magic reduces the effects of magic on a targeted party member. This will decrease the damage taken by harmful spells by X and healing spells by Y. Lasts Z min. Use this to protect party members from harmful spells, but be aware that it will also reduce the effect of healing spells that are cast on them.

Amplify Magic - Amplifies magic used against the targeted party members, increasing damage taken from spells by X and healing spells by Y. Lasts Z min. This would be helpful if you want to increase healing and are not worried about increased spell damage.

Detect Magic - Detects beneficial magic effects on the target for X min. This is an information gathering spell. It's helpful to know what buffs the monster is using so you know how to counter them or know what the monster is capable of. If you can remove those buffs it is even more helpful.

Mage Armor - Increases your resistance to all magic by X and allows Y% of your Mana regeneration to continue while casting. Lasts 30 minutes.

Slow Fall - Slows falling speed for X seconds. You can use this ability to jump from high heights without taking damage. This ability requires a reagent.