Thresh does not gain armor per level. Instead, Thresh collects the souls of dead enemies by approaching them or by placing Dark Passage's lantern nearby. Souls permanently grant armor and ability power. Champions and large minions always drop a harvest-able soul. Small minions only sometimes drop a soul.
A soul will only drop if the enemy unit dies within 1900 range of Thresh. Souls are visible to allies, and only become visible to enemies if the enemy team has vision of Thresh. Souls disappear if not picked up after 14 seconds. 
Cooldown: 18 / 16.5 / 15 / 13.5 / 12
Cost: 80 mana
Active: Thresh throws out his scythe to latch onto the first enemy hit for 1.5 seconds, dealing magic damage and stunning them for the same duration. During this time Thresh cannot attack but will tug on his chains twice over the duration, each time pulling the hooked unit a short distance towards himself.
While a target is hooked, Thresh can reactivate this ability to pull himself to the bound enemy. This removes the stun but allows Thresh to attack again.
Active: Thresh throws his lantern to the target location, which remains there for up to 6 seconds. If an ally right-clicks it, they pick up the lantern and Thresh pulls them both back to his own location. If Thresh moves more than ~1500 units away, the lantern will return to him.
For the next 6 seconds, allies who come near the lantern (even while Thresh is holding it) gain a shield that absorbs damage for up to 4 seconds. Allies can only receive the shield once per cast.
Passive: Thresh's basic attacks deal bonus magic damage on each hit. This value is equal to the total number of souls collected, plus a percentage of his attack damage based on the amount of time since his last attack.
Bonus Magic Damage: Souls + up to 80 / 110 / 140 / 170 / 200% AD
Active: Thresh sweeps his chain in a broad line towards a target direction. Enemies hit take magic damage, are knocked in the same direction as the chains, and are slowed afterwards for 1.5 seconds.
Active: Thresh summons 5 spectral walls around him that last up to 5 seconds. Enemy champions that touch a wall take magic damage and are slowed by 99% for 2 seconds, but break the wall. Once one wall is broken, the remaining walls deal half damage and apply half the slow duration. An enemy can be affected by multiple walls.
Magic Damage: 250 / 400 / 550 (+100% AP)
Remaining Walls Damage: 125 / 200 / 275 (+50% AP)
Maximum Single Target Damage: 750 / 1200 / 1650 (+300% AP)