https://www.youtube.com/watch?v=uZfIP0I73O8

(A small video)

Destruction

Master Level Spells

Fire Blast - Fire Projectile that does 80 damage. Looks like fire breath shout.
Ice Blast - Frost Projectile that does 80 damage. Looks like frost breath shout.
Thunder Blast - Lightning Projectile that does 80 damage. AOE.
Flamethrower - Concentration spell that does 50 fire damage per second. 
Freezing Beam - Concentration spell that does 50 frost damage per second. 
Lightning Stream - Concentration spell that does 50 Shock damage per second. 
Fire Stream - Two Handed Concentration spell that does 75 fire damage per second.
Frost Stream - Two Handed Concentration spell that does 75 frost damage per second.
Ice Coffin - Encases the target in a block of ice.

Vampire Spells

Adept Level
Draining Bolt - Red Projectile that damages enemy and drains health.(40 damage + 20 points absorption)
Expert Level
Draining Blast - Red Projectile that damages enemy and drains health. AOE.(60 Damage + 30 points absorption)

BTW these spells don't hurt followers. And your followers won't friendly fire damage each other with these (Thanks to AFT friendly mod for teaching me this).

Vampire Spells can be brought from Ronthil in Volkihar castle.

Illusion 

Apprentice

Create wolf illusion:- Concentration spell to spawn an illusion of a wolf. Cannot damage or be damaged.
Pacify Animals:- Calms nearby animals.

Adept

Create Skeleton Illusion:- Concentration spell to spawn an illusion of a Skeleton. Cannot damage or be damaged. Carries a weapon that inflicts fear.
Dispel Magic:- Dispel Magic Effects like armor, cloak, candlelight on yourself.
Dispel Magic Others:- Dispel Magic Effects like armor, cloak, paralysis, on target.
Command Animals:- Target Animal will fight for you.

Expert

Create Dremora Illusion:- Concentration spell to spawn an illusion of a Dremora. Cannot damage or be damaged. Carries a weapon that inflicts higher level fear.
Fade Others:- Make the target invisible.

The illusions can be used alongside your summons. But if you have twin souls you can't have two+ summons and an illusion unfortunately. I tried to make it work but failed. 

Master

Obedience:- Commands creatures and humanoids to fight for you. Undead are immune.

Alteration

Adept

Fire Shield:- 50% Fire resistance.
Frost Shield:- 50% Frost Resistance
Lightning Shield:- 50% Shock Resistance
Staggering Blast:- A telekinetic force that staggers the target.
Swiftness:- Makes you swing your weapon faster.
Swiftness Other:- Makes the target swing their weapon faster.
Burden:- Makes the target move slower and swing their weapon slower.
Notorgo's Sprint:- Dash really fast. (Like whirlwind sprint)
Waterwalking:- Walk on water.
Waterwalking Others:- Target will walk on water. 
Slowfall:- Fall damage is halved.

Vampire Spells
Bat Form:- Turn into a swarm of bats to move great distance. Available in lesser power tab. (Like the bat power of VL)
Ronthil sells it.

Expert

Disarm:- Disarm the target, making them drop their weapon.

Master

Diamond Flesh:- Armor Spell 150 power. Effected by Mage Armor perks.
Force Blast:- Telekinetic force to knock targets away.
Slow Time:- Bend time to slow down everyone.
Feather Drop:- Completely negates fall damage.

Restoration

Adept

Cure Disease:- Cures disease on self
Cure Disease Others:- Cure target's disease.

Expert

Hundred Healings:- Heals 10 points for 100 seconds. Like using the novice healing on yourself a 100 times.
Divine Healing:- Heals 200 health on self. No AOE like Grand healing.
Transcendent Ward:- Create a Ward of 100 points.

Master

Celestial Healing:- Heals 300 health on self.
Supreme Ward:- Create a ward of 140 points.

Conjuration

Vampire Spells

Conjure Gargoyle (Apprentice)
Conjure Gargoyle Brute (Adept)
Conjure Gargoyle Seninel (Expert)
Ronthil sells them.

Dwarven Summons
Conjure Dwarven Spider(Apprentice) 
Conjure Dwarven Sphere(Adept)
Conjure Dwarven Ballista(Expert)
Conjure Dwarven Centurion(Master)
Calcelmo sells these.

Apprentice
Conjure familiar horse:- Horse has no fall damage perk.
Conjure Spriggan

Adept
Conjure Armored Skeleton Archer
Conjure Armored Skeleton Fighter
Conjure Armored Skeleton Mage
Conjure Armored Skeleton Warrior
Conjure Dremora Fighter
Conjure Dremora Hunter
Conjure Dremora Mage
Conjure Familiar Sabre Cat
Conjure Spriggan Matron

Expert
Conjure Burnt Spriggan
Conjure Familiar Bear
Conjure High Seeker
Conjure Wisp Mother
Oblivion Walking:- Walk between dimension to become immune to damage and become unable to damage.

Master
Conjure Ancient Frost Atronach
Conjure Pure Flame Atronach
Conjure Charged Storm Atronach
Conjure Dremora Archmage
Conjure Dremora Knight
Conjure Dremora Sharpshooter
Conjure Dremora Warlord
Conjure Familiar Mammoth
Conjure Keeper Archer
Conjure Keeper Knight
Conjure Keeper Warrior
Conjure Lurker
Conjure Spriggan Earthmother


My Other mods

Simple Perk Overhaul

Enhanced Races

Enhanced Standing Stones

Adamant - Elemental Destruction Patch

Stronger Companions Giant

Mysticism Wards Functionality Extended Patch


Credits

Bethesda for making Skyrim and providing the creation kit.
Arcane University and Skyrim Modding hub for teaching me things.