Welcome to my Amumu guide!

Take a seat and enjoy your stay. Coffee and cookies are provided in the comments section. (But you have to comment to get them). ;)

Pros:
- Good ganker
- Deals percentage-based damage
- Cooldown reduces when you get hit
- Cute

Cons:
- Mana pool is a tad small
- Horrible dance
- QQ's a lot. :P

It's quite difficult to provide you with a linear path of items. Therefore, I will have to go into more detail for what to buy and when to buy it.

This will take a bit of brain-cell usage, unlike playing some DPS Carries. (One of the many reasons I love playing Amumu!)

I always start off with a philosopher's stone, in order to sustain my early laning presence. Whenever you feel comfortable leaving the lane, port back and buy a Boots of Swiftness. Once you gain enough money for an Eleisa's Miracle and a item for Sunfire Aegis, head back to base and purchase up.

Now here is where it gets somewhat tricky. You'll need to break down the opposing team into a fraction of sorts. (At least that's how I do it). Also, when breaking it down be sure to classify them by the majority of the type of DPS they output.

Are they 4 or 5 out of 5 Physical DPS? Thornmail --> Sunfire Aegis --> Frozen Heart

Are they 4 or 5 out of 5 Ability DPS? Force of Nature --> Banshee's Veil --> Abyssal Mask

Are they 3 out of 5 Physical DPS? Sunfire Aegis --> Force of Nature --> Guardian Angel

Are they 3 out of 5 Ability DPS? Force of Nature --> Sunfire Aegis --> Guardian Angel

Do they have multiple hybrids? Sunfire Aegis --> Force of Nature --> Guardian Angel

Insert a Warmog's Armor at the end of each build if you so desire. I find that Amumu has a tad low health in end-game, so Warmog's will allow us to beef him up with some steroids.

At the start of this guide I have just listed one possible combination for majority physical DPS opponents. With Amumu you can truly just mix and match different items that contribute to your HP, Armor, and Magic Resistance. Rather than worry too much about getting the exact item build, view it in the sense that what you choose is only crucial in TYPE. In other words, armor for physical-based teams, MR for magical-based teams. It's that simple. There is no KEY item that you need to get if you're against this specific character or any of that nonsense. If you can react based on how and what the enemy attacks with, then you're good to go for tanking, with at least Amumu.

Also, you can add AP into the end of the build if you wish to gain some extra 'Bang!' to your abilities. I would recommend waiting until you at least have 150 of both magic resistance and armor, if against a balanced team. At approximately 200 of any of the defensive stats, you start to experience diminishing returns. This basically means that instead of let's say gaining 1% for every 5 armor you add, you now gain 0.5% for every 5 armor. So essentially you're going to 'cap' out at around 70% damage reduction. (Which is pretty damn good if I do say so myself).

EDIT: Correction, I have recently learned that there are actually no such thing as diminishing returns. However, after you reach approximately 200 or so Armor/MR, it is more COST-EFFECTIVE to start buying HP or AP.

Link: http://www.reddit.com/r/leagueoflegends/comments/h1qpp/attention_there_is_no_such_thing_as_diminishing/

"Only 200? Only 70%? What am I supposed to do now?", you may ask, and to this I say "AP AP AP". The enemy now is going to be hitting you for pretty much nothing, but here's they issue: You're going to be hitting for pretty much nothing too! Like I mentioned last paragraph, without some extra AP you're going to struggle to hold 'aggro' - that is, maintain direct damage focus upon yourself - toward the opponents. That will defeat your entire purpose! We can't let that happen, so late game, rather than a Guardian Angel, you can grab a Rabadon's Deathcap and get to slaughtering those opponents.

A point in Bandage Toss first, for any initial fights that may break out in lane before the minions spawn.

A point in Tantrum second, for the generic Q + E harass combo during early laning phase.

And a point in Despair third. If you have enough mana, you can do a Q + W + E harass combo, or for chasing down a fleeing enemy.

Max Tantrum now, to maximize damage output.

Then max Despair, to melt those tanky enemies.

Finally, max Bandage Toss because you have to max it eventually. :P

Greater Mark of Magic Penetration for a much stronger early game damage output. Helps late game as well, mainly against those DPS carries who don't purchase any magic resistance.

Greater Glyph of Magic Resist so that you have reasonable lane-staying power against AP carries. Also, a majority of champions deal magic damage in some form or another, so it helps no matter who you're up against.

Greater Seal of Armor and Greater Quintessence of Magic Resist for early game lane-dominance. Rather than get Greater Quintessence of Health, I prefer to get these because of the overall percentage-based reduction for damage-intake rather that a flat HP boost.

Why 9/0/21?

Because Amumu functions similar to a caster, with all of his abilities being based on ability power and mana. Therefore it is vital that you spec 9 points into offense for the magic penetration talent, and 21 into utility for all the caster-related bonuses.

Good ol' Flash. The millions of ways that you can use this spell provide it with the most functionality of all the summoner spells. Provides a better get-away than Ghost because when cc'd, ghost loses almost all benefit. Where-as Flash allows for maximum displacement in the shortest amount of time, while cc has no impact on the displacement.

Exhaust for those trouble-some DPS carries that may start wailing away on you with their right-clicking powers. Pop this sucker on 'em and they'll QQ all the way back to base. (In a funeral casket).

Yes, it is. Bye!