Wanted to make a build for Amumu that make him a extremely valuable tank. This build in my opinion has everything to make Amumu an epic tank. He has alot of health and health regen. His armor and magic resistance are really high. But he is also deadly with his high ability power, mana, and speed.

Heal I like to use to escape from group of people to make sure I stay alive or to heal my teammates during a fight.
Exhaust if you are going to gank a lot or slow them down for teammates or Bandage Toss
Flash to escape from ganks or if they are not in range of Bandage Toss
Ignite for when they get away if they low on health this could finish them off for you

I run a 0/14/16. I get defensive masteries to improve your tanking capabilities then mana/health regen to help with you lane longer.

Ninja Tabi instead of Sorcerers is good if there is a lot of DPS
Sorcerer's shoes instead of Mercury's Treads if you really want higher magic penetration.

Bandage Toss
Great skill to start a gank because of the stun effect. Also good when chasing because of long range.I like to follow up with Curse for extra stun. Can be used through walls if they are in range. Very powerful can be used to last hit runners. If you are getting attacked let your enemy chase you to turret and as soon as they are in range bandage toss them so they cant escape. If you are high enough use your ult immediately after to prolong the stun.

Despair
AOE skill great against High hp targets.I do not use it much only when farming or surrounded by many enemies later in the game. But when I do its usually against other tanks Despair can actually do more damage then you are hitting. I still level this last since your mana and mana regen is not very high in the early and mid game.

Tantrum
Great skill I start with this because you will be fighting minions during early game, it is good for last hitting multiple minions(and champions).This is best used after stunning a champion with toss once they start hitting you it cools down faster so you can spam this easily.

Curse of the Sad Mummy
Great ultimate. I follow up [Bandage Toss] with this to make sure they cant get away. I also use to run away when many enemies are behind you use this ult and they will be stunned giving you time to add some distance between you and them and make them think twice about attacking. If too enemies are close by and 1 has low health you if lucky can kill the first with this and then attack the other with Bandage Toss.

Early game

Start with ruby crystal so you have a high amount of health to start or cloth armor if you want to be protected. Either way you are building a Aegis. If you are fighting minions use Tantrum to last hit multiple minions. Once you get Bandage Toss you can harass other champions. You can use Bandage Toss on bushes to attack them but be careful only do it if you know you could kill them and there is not more then 1 in there waiting. If your lane partner is DPS make sure they know that your bandage toss has long range and can stun so you can setup opportunities to kill. Early game you are not really able to kill on your own. You should work on helping somebody more powerful to get the kill.If you are in the middle then if they get withing range of your turret Bandage Toss them so they cant move away and get them to hit you so the turret will help you and attack them.

Mid game

You should be able to dish out and take a good amount of damage.This is good time to try ganks. Again try to find a nice DPS partner to assist you in your ganks so that once you stun them they can finish them off quickly. A strategy I use is when your teammate is coming to gank an enemy bait the enemy into attack you then use your ult to stun them once your teammate gets there they will run. While they are running away Bandage Toss them to stun them again or finish them off.

Late game

You should be able to hold your own. You will have despair now and can push lanes faster. If you are winning by a lot you can probably start ganks and end them before your teammates get there. The game will probably end before you finish building your Frozen Heart. If you are going to gank make sure you can kill them try to gank targets who are already low on health about under 50 percent. A good strategy is if they are near their minions and low on health attack them. While attacking them the minions will attack you and if you are using Tantrum it will cool down quickly making it easy for you to spam it this with Despair should make short work of them. With your high hp, armor, and magic resist you can try a couple tower dives (like Bandage Toss through a wall) but make sure you are not running into a group or you may not walk out.

I don't mind a little criticism since it is my first guide please be constructive