One of the great flaws of the many tank-builds is that amumu haven't got enough influence on the battlefield in regards to damage. He can surely take a hit and stun - which is very useful in teamfights - but he needs some dps.
This build is the one I use for myself, 'cause it makes Amumu more influential, with the extra AP.

FLASH

Is definitively the most important summoner spell. You can't live without it. End of discussion.

As a second summoner spell i usually choose 'cause i like to swoop back to the shop and quickly back into my lane without loosing any experience.
But if you can live without it, i would recommend that since it isn't very useful late-game. As a replacement or would be my recommendation.

Runes

The runes are pretty simple. Amumu is a tank so he gets HP and HP-regen from Greater Mark of Vitality and Greater Seal of Regeneration.

To make him the destructive mummy he has to potentiel to be, he needs cooldown reduction, which he gets from and

Masteries

Many of you might look at the masteries and think it's stupid not to focus the skillpoints on defence, since he is a tank and all. But Amumu don't need the extra help to be a good tank, he needs extra help killing noobs - so the skills primarily focus utility and some offence (to get the extra cooldown reduction, magic penetration and AP)

There is not much to say in regards to picking skills - do as you please.

I like to focus my skillpoints primarily on and Despairsize=20, i do on the other hand stronly recommend to choose -lvl1, early game 'cause it's crucial to both saving your m8's and ganking. (Amumu is a great initiater)

- The first item is the . Very useful in the beginning, as you may take some hits and need to regenerate without recalling.

- Along with the i usually bring a aswell.

- In the beginning it's very important for Amumu to get as many minion kills as possible, so using your to get last hit is absolutely neccesary.

- When you have around 750GP, recall and upgrade your to a Philosopher's Stone. In addition, it's time to get your . (I usually buy a or 2 at this point aswell)

- The last preface item, and probably the most important, is the . This will allow you to farm creeps more efficient with the combo of its aura and your . (Going for some creeps in the forest at this point will boost you additionally - the mana aura gives Amumu the extra cooldown reduction to make him a good DPS)

- Upgrading your boots is crucial. I prefer going fast, so or is my usual choice. But for those who would rather get something more useful from their boots the or Mercury Treads will suffice aswell.

- Making Amumu a good tank, in my opinion, can't be done without .

- Now it's just a matter of getting Amumu some AP, with the and later on

- The Philosopher's Stone can be upgraded into when the need for more HP and the extremely important cooldown reduction comes.

- Philosopher's Stone can also be sold and another more needy item can be bought. e.g. if you are taking alot of damage: might be what you need to get the extra edge.

One thing that many players, as far as I can see, don't take advantage of; is Amumu's Bandage when escaping after being gank'd. A combination of the bandage toss and your flash can pull you across the forest lines by grapping on to forest creeps, or flashing over the tree lines.

Doing that, if you're smart, you should be able to keep yourself from dying.

For example, i often use Baron, or the dragon to escape into the water from the forest, making it almost impossible for the enemy to catch you.