Builds and Runes
Try not to bunch up against his AOE CC ultimate.
Use ranged attacks to kite him around to avoid all of his AoE Damage.
If you can, invade his jungle and steal his blue buff, Amumu consumes a lot of mana while clearing at early levels, so he wont have enough mana to gank or farm.
Ward well to avoid Amumu’s ganks. If you can dodge his Q, the bandage toss is his gap closer, he has no way of effectively ganking.
Don’t dive an Amumu with his Ult up. If he correctly chains his Q with his Ult the stun length will keep you, and your teamamates locked down under tower for a lot of time. This is one of the easiest ways for an Amumu to get fed.