Most of you might think this build doesn't work becouse amumu should only be played as a tank. Well im here to prove that amumu is a great ap/tank. He has a nice AP scale and he can still engage in the fight.

For items I like to start with Doran ring, but Amplifying tome and a HP pot can be an option aswell. Then I go for boots, Sorccerers or Mercurys, but I prefer Sorccerers. Some people might then go for Rylai's, but I like to take Rod of Ages 1st, beacous you get more mana. If you are playing against tanks that stack AP it's nice to get a Void staff for magic penetration. After you build up a nice amount of AP you should get Force of nature, the blue elixr and Banshee's veil. This item build should give plenty of damage survivabilty.

For summoners I like to go with Flash for ganking and escapes, and Exhaust too slow down enemies if you are being chased or if you chase. Ignite is also a good option so you dont rage if someone runs away with 10 hp. You could also take teleport so you just go from lane to lane and farm. You shouldnt take heal beacouse u have enough of survivablity, clarity could be usefull but it gets useless once u get Rod of Ages. Ghost is useless becouse noone should get away when u have Rylai's. Smite, this is not a jungling build. Clarity is completly useless. Fortify, defending turrets is not your job! Rally, what does it even do. Cleanse is not that great while playing AP/Tank amumu. Revive, only noobs use it.

In team fights you can either go 1st or wait for a tank to go in. If u engage you should pop ulti right away. Focus on the AP carry then clean up the rest of the team. When chasing always try to catch your enemey with Bandage toss, but if you miss you can use flash and use Tantrum so you get the slow from Rylai's on him. If that fails too you are doing somthing very wrong. But if you are being chased don't panic. try to juke skill shoots and use Tantrum when an enemey is attacking you, so you slow him and make a clean escape. You can also try using Bandage Toss to grab yourself to a minions and escape over the wall(its usefull when going behind Dragon or Nashor.

While farming use Tanrtum and Despair. You can also get Sunfire cape but it's not that important. You can go solo lane or lane with another champion but always try to get as much last hits as possible. If u have mana problems get a blue buff at about lvl 7 or so. You realy shouldn't have problems with farming.