General Changes
Novice Perk - Scale spell magnitude or duration scales with skill level.
Apprentice Perk - Increase Magicka by 20 points if the Perk Stability is known.
Adept Perk - Increase Magicka Recovery by 20% if the second Recovery Perk is known.
Expert Perk - Increase spell magnitude or duration by 50%. Unlocks perk secondary effects.
Master Perk - Unlocks perk ultimate effects.
Dual Casting Perk - Dual Casting effects works while a staff is equipped. Impact works with staff.

Perks with Secondary Effects
Alteration
Mage Armor - increase armor rating when not wearing body armor by 50/100/150.
Conjuration
Oblivion Binding - Bound weapon ignores 50% armor.
Destruction
Augment Flames - increase fire resistance by 25%.
Augment Frost - increase frost resistance by 25%.
Augment Shock - increase shock resistance by 25%.
Illusion
Quiet Casting - moving is silent.
Restoration
Necromage - reduce incoming damage from undead by 30%
Perks with ultimate effects
Alteration 
Atronach - reduce incoming stagger by 50%.
Conjuration
Twin soul - can summon up to three atronachs.
Destruction
Intense Flames - Power attacks reduce target fire resistance by 75% for 3 seconds.
Deep Freeze - Reduce frost resistance of nearby enemies by 25%.
Disintegrate - Damages nearby enemies.
Illusion
Master of the mind - reduce damage by 80% when invisible.
Restoration
Avoid Death - Restore health per second.

Other Changes
Fire, Frost, Storm Enchater increases spell magnitude of their respective element by 25%.