Hey guys. I recently remember having bought Amumu a long time ago, and decided to pick him back up. After playing lots of games just trying out builds and seeing what his basic fundamentals are, I decided that playing a tank that will just stick to you and smack the life out of you is what he's best at. There was someone who bragged that he was the best Chogath around, but as Amumu, more health can't save you, because of his Despair that can drain life based on a percent. So, without further ado, I present to you my guide.
I buy the quintessence of movement speed, because my first concern is to make sure I can keep up with my target to get a good bandage toss shot on, and to harass with the AoE drain Despair. Magic penetration marks allow me to do more damage with Despair (and I'm going to talk a LOT about Despair, I find it the key in differing Amumu from other tanks) and to make Curse of the Sad Mummy even more painful. Armor and magic resistance are just to play into the fact he's a tank, and those help him early when you can't build tons of armor instantly.
I like the utility tree, and I make the most of it. Lowering death time (because, as a melee tank, death is all but inevitable) to make it less time-impacting, adding movement speed, gold per second (which i find extremely useful, more details in item build) and various others.
You might think my item build is a little strange, but I'll argue why each item is 100% useful:
Heart of Gold: I buy this first. Being Amumu isn't going to give you lots of last-hits on minions without using your abilities, which I save for the enemy champions. This, paired with Greed, give you lots more gold over time, where most of your non-kill gold will come from early.
Boots of Switftness: You need to chase to harass, better aim bandage toss, and to position your ult more easily. Mobility isn't going to help because you want to hit and get your passive in to lower the enemies' magic resist, so swiftness is the way to go.
Frozen Heart: I constantly found myself lacking mana as Amumu, and this is unavioudable. Frozen Heart gives you more mana to succeed, and armor, because you're a tank. The passive is also great.
Abyssal Scepter: Key item in the build. Lowering all nearby enemies' magic resistance makes your Despair and Curse of the Sad Mummy more effective. Also, magic resist = good.
Sunfire Cape: Health + Armor + Passive 35 magic damage per second that doesn't cost ANY mana?!?!? YOU GOT ME SOLD!
Warden's Mail: A component of Randuin's Omen, and since you're going to probably get hit, then the enemy who hit you will try to run away, this is a good item.
Randuin's Omen: I already have a heart of gold along with a warden's mail, combine the 2 for a more stat-producing item.
Guardian Angel: Top it off with a cherry, this baby will make you die less, and in the event you ARE looking at your dead corpse, you will be granted with a magical power that will restore your life and allow you to earn more kills.
All these items are critical in the Amumu idea of "tank slayer"
Bandage toss + Despair is your best friend. Use it to catch up to an enemy, and just smack and harass with despair, they will eventually try to run. Bandage toss them to give them a nice hug, and continue to hug them until they just can't take you anymore and kill themselves. Your Tantrum has a nice passive defense mechanism, which is always appreciated, and your AoE stun Curse of the Sad Mummy gives you an edge in a teamfight. Stop the enemy team for a moment, tell them to chill, and pick off all their AD Carries, like that pesky Caitlyn.
What if you're target is trying to run for cover, as they've had enough of your hugs? BAM! Tell them to chill out with Exhaust, and you can hug them until they're mind explodes. Someone too far to bandage toss? FRAP! Flash toward them, and give them the hug they've wanted this entire fight. Got a teammate chasing someone else that they just can't get up to? KASPLAT! Exhaust that enemy and give them the full load of your Despair. Someone finally get sick of your crying and try to kill you? SHABOOM! Flash away before they go too far with their attacks.
By now you have the idea that I'm saying to take Exhaust and Flash, and you're right! These 2 are optimal for killing and survival.
Now, if you've read through this entire thing, and still haven't gotten hooked on the idea of a tank that can get kills and rarely die, then go back to your Nasus or Shen. But if you DO like the idea, and have success, let me know. If you're doing poorly or end up seeing something I missed, please let me know. Constructive criticism is always appreciated!