Hi, this is my first guide on Mobafire. I'm not English so excuse me for my bad english. In this guide i will explain how i play Amumu. A lot of people play him like a tank and that is good but i think that Amumu is better on an AP build. He really dominate every single teamfight. He can completely change the match with only press "R". And now i'll explain how...

Pros
-Dominate Mid and Late game.
-Powerful ganks.
-Awesome Teamfight.
-Great sustain with Spell Vamp.
-You'll laugh a lot when the enemy team (full life) get insta-killed by your team...

Cons
-Very squishy early game.
-You aren't a really tank.
-Blue buff dependent, early game.
-Vulnerable to counter jungle.
-Sad

Greater Glyph of Potency x9 : Like a mage, with these you will destroy your enemy early game. You will clear the jungler faster, you will gank more efficiently and you will defend yourself from invade.

Greater Mark of Insight x9 : These runes will help you get down enemy tank (and that synergize pretty good with your passive)

Greater Seal of Resilience x9 : Pretty standard on all jungler, they'll help you survive in jungle and get a bit more tanky.

Greater Quintessence of Fortitude x9 : I know, usually only tank take this but with these runes you will be lesser squishy early game and that's important to counter the enemy counter jungler XD

On Amumu i take 9 point in Offense and 21 point in Defense.
I don't think that it's required to say why.
9 point in offense for more AP, CD and some useful MP.
21 point in defense to get more tanky and survivable (plus some other CD)
Of course that build isn't a law, everyone could change it.

- Start with Amplifyng tome and Health potionto clear the jungle faster and deal more damage to the enmy team if you invade their jungle.

- Then take the Boots of Speed and Hextech Revolver to get a good sustain in the jungle and start ganking with the movement speed.

- Take the Boots of Mobility to move faster in the jungle.

- Take a Rod of Ages and a Rylai's Crystal Scepter: These are your core item. You get more Mana, a lot of Health, a large amount of Ability Power and a really good slow with your Tantrum.

- Then finish out the Will of the Ancient to get more ability power and spell vamp.

- Zhonya's Hourglass and Rabadons Deathcap --> A good Armor and an incredible amount of AP. After these items you will deal so much damage with all your ability. Awesome :DD

- Frozen Heart --> Good Armor, Good Mana and Good CD for spam more and more your ultimate.

I max out Tantrum first for the great damage output that help killing, low health enemy champion. Then Bandage Toss for nuke damage and the stun (that is low CD). I max Despair last, but if the enemy team have some very good tank you could max despair second for his damage based on enemy maximum health.

In 1vs1 you go on the enemy with basic attack, toggle Despair and spam Tantrum, if he try to escape use Bandage Toss to stun him and get more advantage on him.

In Teamfight start with Bandage Toss, and then pop all your ability. When your team comes to the battle they only have to fight half life enemy team. GOOD

I hope you like this guide, and i hope my English isn't so bad (D:).
I have really enjoyed playing this build on Amumu and i'm really happy to do something really good in teamfight.

Please if you want to downvote this build tell me why in a comment so i can improve it.