Hi, this is my first build so please be gentle! :3 This is my own personal AP Amumu build which I even go mid lane and win lane. This is a pure AP build with enough bulkness to not be as squishy as the average AP carry. If you think this build is crazy, then you're calling all the Singed builds with pure AP crazy too. This is because pure AP on Amumu is good for his 1:1 ratio scaling on his Bandage Toss and Curse of the Sad Mummy. Amumu is my favorite 1v1 champion because of his stun/snare from Bandage Toss and Curse of the Sad Mummy, and also because no one will expect Amumu to do so much damage in a 1v1 anyway. Usually, I end up dealing half of the enemy HP after stun wears off. I've also carried several games with this build and even a ranked!(Yes, I had low ELO at the time) Also, this build doesn't need another tank in addition to Amumu, but having bulky champs on your team is usually good anyway. If you have any questions or ideas to improve this guide please comment below!

Pros: High damage output
Hard to escape from
Unexpected
Fun!

Cons: Not as bulky as you may like
A bit tougher to live once you initiate team fights
Team will most likely call you noob and QQ hard if you don't carry

I get basic mage runes Greater Quintessence of Health, Greater Mark of Magic Penetration, Greater Seal of Armor,and Greater Glyph of Cooldown Reduction. The build really needs Greater Mark of Magic Penetration and Greater Glyph of Cooldown Reduction because of the magic penetration (not much other marks you can choose) and cooldown reduction.

The Greater Quintessence of Health and Greater Seal of Armor can both be switched out for Greater Quintessence of Magic Penetration Greater Quintessence of Scaling Ability Power Greater Quintessence of Ability Power Greater Seal of Scaling Mana Regeneration Greater Seal of Replenishment Greater Seal of Ability Power. The list can probably go longer but I think you get the point now. I just prefer what I use and it works. Also, I don't have enough IP for runes right now anyway.

Basic offensive masteries for AP carries. You can probably change some for something else, but these are usually preferred.I max Good Hands rather than Perseverence because 4% of 22.75 is .91 not worth even putting points. Also, even though I usually don't plan on dying, I enjoy actually being on the map and helping the team longer if I do in fact die.

So, first I start out with Doran's Ring, but you can start out with any other item that gives AP or mana regeneration like Meki Pendant or Amplifying Tome. I simply just like the fact that Doran's Ring gives both AP and mana regeneration so I start with it.

You can choose to get Catalyst the Protector before Boots or after Sorcerer's Shoes. It really depends on the situation or how you are doing in lane. You can also switch Sorcerer's Shoes for Ionian Boots of Lucidity or Boots of Swiftness if you really want either over Sorcerer's Shoes.

The core build is Doran's Ring, Sorcerer's Shoes,and Rod of Ages, but grabbing a Rylai's Crystal Scepter is really nice for the slow and more HP. Void Staff is also an item you can get for more damage if you need it. After the core, you can choose to go more tanky with Warmog's Armor, Sunfire Aegis, Thornmail, or any other tank item. I think that his passive on Tantrum is good enough for some basic armor in addition with Greater Seal of Health

You can also grab a Hextech Gunblade if you want to super push some lanes. This can also lead to getting an easy kill for yourself if the enemy team just sends one person to stop your backdoor because "It's just Amumu! How much can he do?" A Hextech Gunblade with blue buff is just amazing for 1v1 with its active and spell vamp/life steal and can just push lanes pretty fast without taking any damage.

Remember, NEVER BUILD STATIC BUILDS. Always change your build to what the situation of the game is.

I prefer getting Flash to escape and also you can Flash towards fleeing enemies then Curse of the Sad Mummy and Ignite just for an extra damaging skill. You can also get one of the following:

Ghost: This spell is just really good for chasing people and slowing them using Despair stacked with Rylai's Crystal Scepter. Also, you can use it for escaping.

Exhaust: You can use this to keep people in your slow when you haven't bought Rylai's Crystal Scepter yet and it's also good to help your 1v1 game because it lowers the target's AD and AP.

Clarity: If you are really having problems with your mana or just plainly have an itchy "trigger finger" for spells, then go and get it! Usually I just grab blue buff if I need some mana regeneration and cooldown reduction.

Teleport: Easy way to backdoor, catch up to team, defend towers, etc.

Fortify: This is a damage build so you probably would want to be getting kills and assists rather than supporting team. This summoner is underused anyway.

Farming may seem tough early in lane, but once you get that catalyst you should be pretty fine in lane if you don't spam Tantrum on every minion wave. You can probably grab blue buff past level 6, but that's your choice. If your team isn't 100% dependent on you, try to clean up heavily pushed minion waves coming in.