Hey guys, back with my second build, and well, amumu has been meh baby since the beginning of league, He's a very fun champion to play :D. Plus, as a tank, you will win alot more games then usual. Tank amumu is obviously the way to go, but be careful, he's among the, "squishier tanks"

Pros:
Amumu is probably the best initiater in the game
Great amount of cc
Can put out alot of AoE damage

Cons:
He is fairly squishy for a tank
Very low range
horrible in the laning phase

So, i like to start out with a regrowth pendant and mana pot so i can lane until level 6. because let's be honest guys, amumu is a fail sauce laner. if you have a good lane partner though, you can still pull off some kills so you can get some farm. Tanks are very expensive to start out :O.
Then when you recall, you definetely wanna get philosopher's stone to fix all mana problems that amumu has so badly. Then, for boots i like getting boots of swiftness, i feel them to be extremely necessary for amumu, since his job is to get in their faces.

After boots, Sunfire cape is boss, like i said, your job is to get in their face. and well, sunfire cape is very nice for that, plus its a very tanky item as well.

Banshee's veil is awesome, hp, mp, magic resist adds soem tank to amumu, Plus. you will be able to lock them down with no interference. Imo, Banshee's veil is among the best items in league

Sometimes during team fights, you go in ulti. their whole team dies... but you die right as you go in. Guardian Angel will save you from that completely. initiate, Ulti, Die, their team dies, you revive. and then you push their turrets for a win

After guardian angel, (most games don't last this long) i like to get force of nature or thornmail depending on their team, if they have a fed yi, or other physical auto attackers, thornmail. if they have alot of casters, then go with the force of nature

For runes i like to get alot of mana regen, and some ap or magic pen. Amumu has hard mp problems, and the more mana gen = more tantrum spam/ tears. the magic pen is just for the lil' bit of extra damage in the team fights/ ganks. For quints i like raw health and mana for the early game, since he has probs.

Masteries. For masteries i like 0/21/9, well, obviously. he's a tank ^.^. i put the extra 9 in utility for the mana regen :D

Bandage Toss: right away i like to get bandage toss for beginning kills. but then i don't need it until i'm forced to ;).. anyways, bandage toss throws a bandage at the enemy, if it hits then you fly at the enemy, dealing damage and stunning for 1 second. this is what makes Amumu such a good initiater.

Despair: Amumu cries ;(.. but, it deal percentage of health t enemies near him, which is super boss. costs mana / s. I like despair, but i feel tantrum is more useful early game, so i don't get it much.

Tantrum: Another AoE spell that deals damage and reduces physical damage taken. the more you get hit, the llower CD it is. making it a great farm ability. I love this move. deals a fair amount of damage. i try to max it out right away :D

Curse of the sad mummy: Amumu has one of the best ultimates in the game. it's what makes him a good tank/ team player. it's an AoE that snares enemies and doesn't let the their team attack for 2 seconds, PLus, it does damage :D
I get it every time it's up... obviously :)

I like to go with Flash and Ignite... Flash for getting away / initiating, and ignite.. because i like damage ;).

Exhaust: exhaust could definetely replace ignite. slows enemies for more successful ganks. + makes it hard for "fed people" to kill you or a teammate.

Teleport: honestly. this should be here instead of ignite. but i still really think ignite is awesome. teleport will help you protect lanes and get back to help your team after recalling.

Cleanse: cleanse is obviously good. but banshee's veil is good enough for me :D

Early game: Just play it safe. try to farm, but if they are harrassing you, maybe ask for a gank here or there. and the most important thing here is to A. not die and B. Protect your turret. You wanna lane witha hard dps. if you do. getting kills in the lane should be fairly easy with bandage tosses :D

Mid game: When you get your ulti you are very deadly. If your lane is'nt going anywhere, then go gank get your carry kills, then push their turret. but remember. your turret is more valuable then a a kill. so only gank if your partner is doing fine 1v2 for now.

Late game: Late game is amumu's strong suit. because now he actually has some tank items. when team fights show up.. DONT BE SCARED, tell your team, "when i go in, RAPE THEM"
then you bandage toss. flash if needed, ulti, spam abilities and run in circles. and your team should do the rest. Remember. if you get an ace or 3 or 4 of them.. psuh a turret. don't be babies

Amumu is my all-time favorite champ, he's one of the best tanks in the game, and your team will love you. If only he wasn't banned every ranked game xD, i still recommend him, he's a bit difficult to play, but he's only 1350, and he is a BOSS.