I first played Amumu as a very new summoner at level 8. I owned no champions, played him when he was free, and instantly took a liking to his aggressive tanking style. His Tantrum lets him turn his enemies' attacks against them, and shreds through minions like crazy. Despair gives him an aura that deals both straight damage and percentage health damage per second to nearby enemies, which is devastating to tanks and large creeps like the Ancient Golem, Lizard Elder, Dragon, and Super Minions. His Bandage Toss is a skill shot with a 1:1 AP ratio and a powerful stun which, combined with his ridiculously overpowered high-damage AoE 2.5 second snare ult ( Curse of the Sad Mummy) gives him some of the best crowd control in the game.

Most of the time when you see an Amumu at level 30, especially in Ranked and Draft Pick, he's in the Jungle (Dominion aside...that's a guide for another day). Using this build you can do massive damage, serious CC, and still be a formidable tank, allowing you to gank effectively and quickly, cover for allies, and tower dive with devastating effect.

Amumu stomps his way through small creep camps in the jungle with incredible speed and efficiency, so with just a Regrowth Pendant you almost always have enough health to gank or pick up buffs.

Magic Pen Marks ~ These are mostly for your late game. These will let you keep on tearing through carries and off-tanks alike as if they had 0 Magic Resist, and will keep pretty much any tank but Galio below 100 adjusted MR.
~*~Alternatively~*~ Attack Speed Marks - These will speed up the rate at which you can apply your passive, as well as improving your attack damage per second to be a little more potent. If you're having trouble early game try these instead and remember to cycle your basic attacks between targets. With a full set of these you should be able to keep 4 or 5 targets debuffed at a time. NOTE: If you're going to substitute in a Malady for any item in this build, make sure you're using these marks instead of Mag Pen. (especially since Magic Penetration, unlike MR shred, doesn't get benefits below 0 MR)

Flat Armor Seals - Reduces the damage you take from minions. Not much reason why you'd get anything else when jungling.
~^~Alternatively~*~ I haven't tried it, but in theory HP/5 seals would probably work fine. I'll pick some up and update this when I get a chance, or if someone else wants to try it and let me know how it goes that would be rad.

CDR/level Glyphs - Amumu's ult rocks face, but the cooldown lasts for-freaking-ever. You really want to maximize your CDR with Amumu because it means you're laying down more crowd control, dealing more damage, and actually utilizing your huge stores of mana and significant mana regen late game for more than just keeping Despair on.

Flat AP Quints - I use flat AP quints personally, but there are tons that would work just as well. Movement Speed, CDR, AP/lvl, Gold/10, HP/5, MP/5...the list goes on. Use your quints to tweak this build to work best for you.

Offense [0] - No points in offense. There's not much here for an AP jungler.

Defense [21] - Tough Skin - last longer in the jungle, great with Tantrum
Summoner's Resolve - shouldn't have to explain this one
Bladed Armor - stacks great with Tantrum and speeds up your jungle time. Also great for Heimerdinger's and Shaco's turrets. NOTE: If you're tanking a buff (red buff for an AD carry in lane, for example), this can accidentally steal it if the target is too low health. Watch your targets' health closely in cases like this.
Indomitable - reduces incoming damage from everything. Can't go wrong there for a tanky jungler like Amumu; stacks beautifully with Tantrum's damage reduction.
Enlightenment - Gives you some much-needed CDR, especially getting towards higher level. This will make you formidable in late game teamfights with your Tantrum and allow you to use your Bandage Toss to both initiate and chase.
Mercenary - Since you should be focusing on getting your carries fed rather than taking kills yourself, it's important to get a lots of assists. This will keep your gold up there with the carries even if you're only getting assists all game.
Juggernaut - It's essentially stackable Tenacity with a fat chunk of extra health. It's a sweet deal.
Initiator - With your health regen, you'll actually spend most of the game pretty much around full health except for some early jungling. This is a great move speed buff for ganking and getting back into the fight after a recall. It also is suggestive of one of Amumu's core roles: initiating! If you time your Heal right, this can also work as a move speed buff coming out of a losing fight.

Utility [9] - Runic Affinity - Arguably your single most important mastery as a jungler. Extends your Blue Buff and Baron Buff. This also works for the Storm Shield and move speed buffs in Dominion!
Improved Recall - The warrior who runs away lives to fight another day. Shortens recall time. Get back in the fight 1 second earlier every time, quicker response time to backdoors, better chance of escaping from behind enemy lines...this is just a really great ability to spec into in general.
Expanded Mind - Amumu's got some serious mana issues, especially early game. This will help keep you from running out of mana for that critical Bandage Toss or Curse of the Sad Mummy in a teamfight, as well as reducing how often you have to go back during the Jungling phase. It also scales really well into lategame to pump your Archangel's staff.
Swiftness - High Move Speed will let you move between creep camps and lanes quickly, as well as improving your ability to escape.

This build is constructed around a few basic items:
Regrowth Pendant - In the jungle, you gain a lot of health over time from these. With these you can gank or cover after your first pass through the jungle. You won't have your rope yet, but you can quickly get it by leveling up on a couple minions or a wraiths if covering for mid.
builds into: Force of Nature
Sapphire Crystal & Meki Pendant - A well built Amumu handles like a steam train. That steam train doesn't stop going for anything until it runs out of fuel. For Amumu, fuel = mana. Your mana is what makes you dangerous, and if you drop below 200 you're not going to be able to slaughter your foes effectively.
builds into: Archangel's Staff; Frozen Heart
Cloth Armor & Chain Vest - stack some heavy armor up as soon as you can, just don't let it stop you from finishing your Force of Nature
builds into: Frozen Heart
Negatron Cloak - Some of the biggest threats to effective ganking are other AP tanks and carries. Shrug off their stuns and nukes with hefty Magic Resist.
builds into: Force of Nature; Abyssal Mask
Blasting Wand - Surviving is great, and Amumu has some good CC to keep enemies' attention drawn, but he's most potent when he can also lay on hefty damage with his Tantrum, Despair, and Curse of the Sad Mummy during fights, and having a 1:1 AP ratio skill shot stun is another great reason to build some often overlooked AP on this champion.
builds into: Archangel's Staff; Rylai's Crystal Scepter; Abyssal Mask
Giant's Belt - Health is happiness. With 200 MR, Madred's and other percent health damage isn't very intimidating because it's almost all Magic Damage, which you heartily ignore. Lots of Health will let you ignore that nasty True Damage too.
builds into: Rylai's Crystal Scepter

Start with: Regrowth Pendant and Health Potion

Work on finishing your Tear of the Goddess and boots ASAP, then finish building Force of Nature. You should also buy wards as needed. You shouldn't need any potions after the first one.

As you get into mid game, start working on Frozen Heart and Rylai's Crystal Scepter, starting with Chain Vest or Giant's Belt respectively. Teamfights start here so you'll need to start being tanky. As soon as you're done with those, start working on Abyssal Mask. When you have free item slots, keep buying wards and make sure you have vision around Baron, Dragon, and both teams' blue buffs.

Getting into late game, finish your Archangel's Staff (should be pretty much fully built at this point) and then you may want to consider deviating from this build a bit. If you're carrying for AP damage pick up a Rabadon's Deathcap (AP Amumu is a frightening thing indeed). If there's one enemy who's always getting away from teamfights, start working on Deathfire Grasp and use that Active when you initiate (if you get Ionian Boots, keep in mind that you'll be wasting their CDR if you do this). If you feel like you need to be doing more damage to towers and inhibitors or need some more move speed, get Lich Bane. If they're AD heavy, get Thornmail. If your team's AP heavy or teamfights are long and drawn out pick up a Will of the Ancients. Keep your final item choice dynamic. Think about it thoughout the entire match and make it really count.

**Don't buy Sunfire Aegis. It's a great item on Malphite, Leona, Alistar, or any other true tank. On Amumu it's a waste of an item slot. I die a little every time I see someone using that item instead of Abyssal Mask or Rylai's Frozen Scepter on Amumu. Madreds Bloodrazor on a Caitlyn, Ashe, or Kog'Maw will end you. If you need Armor, build Thornmail.**

!!!Why Archangel's Staff?!!!
Despair consumes 8 mana per second when it's turned on. With this item on top of Amumu's normal regen at level 18, you regenerate 8 mana per second. In other words, this one item solves your mana problems completely and utterly. Also, with nearly 3000 mana, it's one of the best sources of AP you can possibly own. As a tank, it's important for your team to be able to rely on your crowd control and ability to hold down aggro. Force of Nature means you'll never have to go back for health, and Archangel's Staff means you'll never have to go back for mana.

~*~BOOTS~*~
Sorcerer's Shoes - Great for if a team is spec'd into MR heavily.
Mercury's Treads - If the enemy team has a ton of CC, get these and eat it up like it's cake. Delicious cake.
Ionian Boots of Lucidity - If you sub out Frozen Heart for something else and need to get something else for the CDR, these boots are a cheap way to do it. Remember though: CDR caps at 40%.
Boots of Swiftness - Move speed is always a good thing. If you don't need Tenacity, Mag Pen, or CDR, get these.

**coming soon ~ UPDATE: Had to format my hard drive with all my screencaps, so I need to go through and get them all again. This section will happen eventually.**

INITIAL PATH: Blue -> Wolves -> Wraiths -> Golems -> Red -> Wraiths** -> Wolves ((** ~ You should hit level 4 right after killing Red using this path. This is a great time to take your first level in Bandage Toss and gank)).

After ganking, if you still have plenty of health you can go for another gank. If your health is low you can go to Wraiths for some easy health, move on to Wolves, gank the near lane, then grab Blue again when it spawns at ~7:20 (make sure you have at least 200 or so mana when you start fighting him at this point so you can afford two tantrums to kill the small lizards and keep Despair up long enough to get the Golem in smiting range (<600 health). At this point you can either finally go b, or you can KEEP JUNGLING AND GANKING. With healing sigils and blue buff, you almost never have to go back. It is important to get wards and grab your boots and Tear of the Goddess though, so I recommend going back once you have about 1500 gold so you can buy basic boots, TotG, and a couple of sight wards.

From there it's your call. Get blue as much as possible, but share it with your teammates when they need it. Your Tear of the Goddess solves your mana problems pretty much indefinitely. Steal the enemy's blue when it's safe to do so, but pay a lot of attention to the map when you do. Save your Bandage Toss and if the enemy jungler shows up hit them right as they get to the bush, basic attack them, move back towards the golem, hitting both the golem and enemy jungler with Tantrum. Watch the Golem's health closely and Smite it as soon as it gets to a point where you can do so. If you're getting owned by the enemy jungler though, just get out of there. You can also use your ult to kill the golem while doing a ton of damage and CC to the enemy jungler, allowing you to just walk away with the enemy's blue buff, but it's best to save your ult for teamfights when you can.

NOTE: When this build is finished, blue buff is almost completely useless on Amumu since you have about 38% CDR and 40 mp5, so give it to teammates whenever possible in mid-to-late game.

~*~INITIATING~*~
Don't feel like you always need to use your Bandage Toss to initiate ganks. If your opponents are overextended (as they should be if you're ganking) you can often come around behind them, tag each of them with a basic attack, Bandage Toss the carry who's usually running away by now, Tantrum again, and your Despair and Carry(ies) should be able to pick up the kill(s). If someone in the lane has a flash, try to wait for them to burn it before you Bandage Toss them.

Sometimes, however, you will want to use Bandage Toss to initiate. If you have a clear shot from cover and your teammates are there to capitalize on your stun, go for it. Just keep in mind that early game, when the outer turrets are still up, your cooldown will be too long to use it twice in one fight unless your opponents for some reason don't run right away (I'd monitor the bushes for their Jungler or any MIA's in such an instance), and you may need to use your ult to pick up the kill if your opponents start to run away and have a flash or a jump of some sort to get out of your Tantrum and Despair range.

~*~Sharing Is Carrying~*~
It's best to let your carries have a few kills early so they can hold their lanes while you continue to jungle. Don't worry about getting starved if you start out 0/0/7 or something; you still get pretty fed off of Assists with Mercenary fully spec'd, and you'll continue to get a lot of assists and win a lot of games if you let your teammates rush key items like Rabadon's Deathcap and Bloodthirster

~*~Cover Your Solo Lanes~*~
Every few minutes, offer to cover top and mid for just long enough for your solo laners to buy some items, heal, and get mana. Use your Despair and Tantrum conservatively and avoid tanking minion damage except to protect towers so you can move to gank, take blue/dragon, or just continue jungling without having to go back. There are some large purchases in this build, so you don't want to go back too often or you'll wind up with nothing but wards.

Tantrum, Tantrum, Tantrum. This skill is amazing. Grab a rank of Despair at level 2, Bandage Toss at 4, and Curse of the Sad Mummy at 6. Max Tantrum, put a couple ranks in Despair, level up ult whenever possible, and wait until endgame to level up that Q. Despair and Tantrum both keep the same mana cost at all ranks while significantly gaining damage, as well as lower cooldown and more damage blocking from Tantrum.

Why Tantrum? Reduces damage from monsters in the jungle, turrets (if you aren't comfortable turret diving, get that way), creeps, and enemy AD carries. Stacked with your masteries, nearly 200 armor, and Force of Nature, you can eat turret damage for quite some time late game because of this skill, in addition to taking much less damage from jungle creeps early game.

Bandage Toss is important to put one level in at level 4 and no more until it's the only thing you can level up. This skill will eat your mana up if you try to level it early game. Let it come out and dominate late game and otherwise be an initiator for ganks that allows your team to get fed.

Smite - don't try jungling with Amumu without this skill. Simple as that
Heal - out of all the summoner skills, Heal is the only one that got buffed with the new patch. It's really quite good now and will let you persist in the jungle, against Baron, tanking towers, and in teamfights. Also, you can drop it during a gank to heal yourself and teammates to turn a bad or sub-par gank into a lossless double kill for your team.

~*~Alternatively~*~
Ignite - if you can find a way to spec into the offensive tree, this is a great way to play aggressively. Doesn't really suit this build very well though.
Flash - never really a bad choice, but it got nerfed quite a bit for Season 2 and won't do anything for your jungling speed or sustainability in combat. Great for ganks and escapes, especially on Baron and Dragon.
Surge - both the Attack Speed and AP buffs will speed up your jungling as well as add some potency to your ganks. I haven't used it myself yet because everyone else seems to think it's terrible and threatens to report me for feeding if I even mention it, but I'm sure it could be quite useful for an aggressive Amumu jungler. You'd probably want to spec more into offensive if using this skill though so you can use the improved version
Exhaust - Amazing for ganks. Also great for if an enemy Udyr or Lee Sin shows up in your jungle.

***I'm only 1211 ELO, but I have an 80% win rate and 3.1:1 KDA in ranked with Amumu, making him by far my best champ in ranked, so hopefully this information is relevant and helpful to you. If your ELO is significantly above or below 1200, some of this advice may not apply***

The main difference you're going to run into when playing ranked is that people will ward like crazy and push a lot less, so ganking will be much more difficult. An early game Oracle's Elixer can help a lot. Hunt down and destroy wards, then place your own and LEAVE THAT LANE. Once you're confident that a lane is no longer warded, hang back and clear out the nearby jungle and be ready to gank as soon as possible. Instead of coming up the river to gank, come through the enemy's jungle when possible. Remember to save your Bandage Toss; it's much harder to dodge at point-blank range than at full range and much more effective with teammates there to deal damage than if they aren't.

If someone on your team has Teleport, try coordinating ganks against tough targets with their Teleport so that you can CC the target while your teammate teleports in. This might even mean dropping a premature Curse of the Sad Mummy to keep a single high-priority target in ranged, but a lossless kill is worth it in ranked.

Be very careful about intruding into the enemy jungler's turf. Use wards to scout the surrounding area so you can see when they're coming. Don't even both taking blue unless you have an Oracle's. Find their ward, kill it, and drop your own. Go hide nearby and wait for them to show up and start taking blue, then steal it. Try to stun your opponent right before the Golem gets to smiting range and smite it yourself before killing off your opponent.

NEVER go into the opposing jungle with missing health/mana unless you know exactly where the enemy jungler is or you're 125% certain that you can beat them 1v1. Keep an eye on lanes. MIAs generally mean you're about to get 2v1'd, so get out IMMEDIATELY if an MIA is called in an adjacent lane.

Ward Dragon at level 4 and keep it warded as long as its alive. Baron Nashor and Dragon are excellent places to use Vision Wards if you don't have an Oracle's Elixer active since they'll generally be warded. If you do find a ward, don't stay around for longer than it takes to kill it.

Ganking MIAs can be an effective way of making up for lost ganks due to enemy wards. When a teammate calls an MIA, if you can get to the river and ward the centermost bush, you can often catch an opponent when they're extremely vulnerable and nowhere near a turret. Make sure to coordinate such a gank with teammates so you can be sure you don't get outnumbered. Again, making use of a teammate's Teleport via your ward can be a good way to ensure your gank is successful and lossless.

When taking out minions in lane, make sure you're ahead of your minions so you're taking aggro from as many enemy minions as possible. This not only means that your creep wave will be stronger when it pushes forward; it also means you'll be able to cast Tantrum more often and secure more minion kills, while also building your Tear of the Goddess faster.

When moving through the jungle with Blue Buff on, use your bandage toss to get over walls faster. This even works for Baron and Dragon.

Remember to hit as many minions as you can with your basic attacks. Cycle your attacks systematically so the debuff is applied to all of your targets. (don't do this with wraiths; just keep attacking the big one)

If you hit a minion and it just barely survives, you can turn on Despair real quick and sometimes it'll pick up the last hit. You should generally have despair on whenever you're in combat though unless you're low on mana.

Amumu's now available in 4G:

Good luck; have fun
Gank
Get fed
Good game

Thanks for reading my first guide to my all time favourite champ. If you find something you don't like, please leave a comment before downvoting and I'll do my best to address it.