The school of Destruction involves harnessing the energies of fire, frost and shock. This skill makes it easier to cast spells like Fireball, Ice Spike, and Lightning Bolt.

The destruction tree is good for an offensive mage,or any mage that wants to use high damage spells. Non-mage classes won't benefit much from this tree.

The Destruction skill can be leveled up by using destruction spells a lot to damage and kill the enemies. You can also level destruction up by visiting a trainer and paying him to train you.

TRAINERS
Journeyman Trainer: Wuunferth the Unliving (Windhelm)
Expert Trainer: Sybille Stentor (Solitude)
Master Trainer: Faralda (College of Winterhold)

SPELLS

Novice:
Flames: A gout of fire that does 8 points of fire damage per second. Targets on fire take extra damage.
Frostbite: A blast of cold that does 8 points of damage per second to health and stamina.
Sparks: Lightning that does 8 points of shock damage to Health and Magicka per second

Apprentice:
Fire Rune: Cast on a nearby surface, it explodes for 50 points of fire damage when enemies come near
Frost Rune: Cast on a nearby surface, it explodes for 50 points of frost damage when enemies come near
Firebolt: A blast of fire that does 25 points of damage. Targets on fire take extra damage
Ice Spike: A Spike of ice that does 25 points of frost damage and stamina
Lightning Bolt: A Bolt of Lightning that does 25 points of shock damage to health and half that tomagicka

Adept:
Chain Lightning: Lightning Bolt that does 40 points of shock damage to health, and half that to Magicka, then leaps to a new target.
Fireball: A Fiery explosion for 40 points of damage in a 15 foot radius. Targets on fire take extra damage.
Flame Cloak: For 60 seconds, Opponents in Melee range take 8 points of fire damage per second. Targets on fire take extra damage.
Frost Cloak: For 60 seconds, opponents in melee range take 8 points of fire damage and stamina per second
Ice Storm: A Freezing Whirwind that does 40 points of frost damage per second to health and stamina
Lightning Cloak: For 60 seconds, nearby opponents take 8 points of shock damage and half that in Magicka

Expert:
Icy Spear: A Spear of Ice that does 60 points of frost damage to health and stamina
Incinerate: A blast of fire that does 60 points of damage. Targets on fire take extra damage
Thunderbolt:  A Thunderbolt that does 60 points of shock damage to health and half that to Magicka
Wall of Flames: Sprayed on the ground, it creates a wall of fire that does 50 points of fire damage per second
Wall of Frost: Sprayed on the ground, it creates a wall of frost that does 50 points of frost damage per second
Wall of Storms: Sprayed on the ground, it creates a wall of lightning that does 50 points of shock damage per second

Master:
Blizzard: Targets take 20 points of frost damage for 10s, plus stamina damage
Fire Storm: A 100 point fiery explosion centered on the caster. Does more damage to closer targets
Lightning Storm: Target takes 75 points of shock damage per second, and half that to Magicka

PERKS

Novice Destruction
Cast Novice level spells for half magicka

Apprentice Destruction
Cast Apprentice level Destructions spells for half Magicka
Requires: Novice Destruction, Destruction 25

Adept Destruction
Cast Adept Level destruction spells for half Magicka
Requires: Apprentice Destruction, Destruction 50

Expert Destruction
Cast Expert level destruction spells for half Magicka
Requires: Adept Destruction, Destruction 75

Master Destruction
Cast Master level destruction spells for half Magicka
Requires: Expert Destruction, Destruction 100

Note: The novice, adept, expert and master destruction perks are a MUST for anyone planning to use Destruction as his primary or secondary tree skill

Destruction Dual Casting
Dual casting a destruction spell overcharges the effect onto an even more powerful version.
Requires: Novice destruction, Destruction 20

Note: Great perk which increases damage output by a lot
To Dual Cast a destruction spell,  equip the same spell on both right and left hand, then press and hold both buttons to cast

Impact
Most destruction spells will stagger an opponent when Dual Cast
Requires:  Destruction Dual Casting, Destruction 40

Rune Master
Can place runes five times farther away
Requirements: Apprentice Destruction, Destruction 40

Augmented Shock (1/2)
Shock Spells do 25%/50% more damage
Requires:  Novice Destruction, Destruction 30/60

Augmented Frost (1/2)
Frost Spells do 25%/50% more damage
Requires: Novice Destruction, Destruction 30/60

Augmented Flames (1/2)
Fire Spells do 25%/50% more damage
Requires: Novice Destruction, Destruction 30/60

Disintegrate
Shock damage disintegrates targets if their health is low
Requires: Augmented Shock, Destruction 70

Deep Freeze
Frost damage paralyzes targets if their health is low
Requires: Augmented Frost, Destruction 60

Intense Flames
Fire Damage causes targets to flee if their health is low
Requires: Augmented Flames, Destruction 50