Hi everyone I am King Odarth, this is my first real guide and I wanted to share this with the community.

Amumu is a champ I bought early in my LoL life. It was a little hard to understand his mechanics at first but after 2-4 games he was a breeze and an easy win. Failing with Amumu is relatively hard since he only has one skill shot and 3 AOE abilities.

I use smart casting when playing him as it saves a lot of time when using his Bandage Toss and if you find it hard too see how far it goes, just enable smart casting show spell outline in settings below your smart casting options.

For Amumu, I suggest this Jungle pattern.

Blue Buff - Smite - Wolves - Wraiths - Red Buff - Smite - Gank

Or

Blue Buff - Smite - Wolves - Wraiths - Red Buff - Smite - Wolves - Wight - Smite - Gank

Pros

Powerful Late and Early Game
Deadly Ganks
Fast Jungle Clear
Snowballs well
Easy to Master
Great Team fighter

Cons

Cry's alot!
Needs Friends
Must land Bandage Toss to be fed well
Subject to KS'ing

Amumu is most probably one of the cheapest and best Team Jungler, quite similar to Hecarim in play style I find. When ganking a lane always ping for your team mates to engage and Crowd the target first so it is easier to lane your Bandage Toss then activate your Despair then you Tantrum. If the enemy still isn't low enough use your Curse of the Sad Mummy for a kill secured. Never use your ultimate to early and neither should you neglect using it, this is what separates the good Amumu from the pro's.

Curse of the Sad Mummy is Amumu trade mark as it is quite a table turner. It can be used to escape, chase, tower dive, and pick off easy kills by yourself. If used with Zhonya's Hourglass in a team fight then that is one very well won team fight if your team follows through properly.

Amumu is a troll Top Laner because many people are unaccustomed to playing against him top. He can easily zone your opponents such as Lee Sin since many top laners rely on being close to farm. Try to have your Despair on only when in the midst of the creeps. It drains mana very quickly that's why I sometimes take the Crystalline Flask for the mana sustain. Amumu early game is really powerful with the high damage he deals. Try to get to lvl 6 before the enemy especially against champions like Garen because of the devastating power of his Demacian Justice.

When an enemy attacks you combo him in this order. W,E,Q,E,R then E again by then the enemy would more than likely be dead. But try to poke him when he comes close and hold your Ultimate for when your jungle ganks or too prevent yourself from being ganked.

Cursed Touch reduces magic resistance by up to 25. When going for the kill, make sure you get in at least one melee attack, as many champions only have 30 base magic resistance.
Refrain from spamming your skills early game, as it can lead to mana starvation.
Maxing Bandage Toss last allows you to stack up damage with your other abilities early game. The length of the stun is the same at all levels of the skill.
Bandage Toss can also be used through walls on neutral camps as an escape mechanism.
The Ancient Golem buff allows Amumu, due to its mana regeneration, to keep Despair activated almost indefinitely.
Despair is very effective against other tanks, so make sure you're in range of the opponent's highest health champions.
Despair has a 0.01 (1%) scaling. In game the tooltip only shows despair doing more % health damage per every 100 ability power. For example 500 AP = 5% health every second + 2.7% base and 24 additional MD at level 5.
Tantrum passive makes Amumu a very hardy jungler.
Amumu is a great jungler with Despair and Tantrum allowing for an easy and strong jungle.
Amumu's pre-level 6 ganks are fairly strong, provided the lane is pushed. A pushed lane, teammates with closers and good damage or teammates with 2 or more Crowd Control abilities can often result in a kill, even against enemies with Flash. The key is to hit Bandage Toss successfully for the stun, and pre-level 6, you will often only have 1 chance to do so. Bandaging from a bush straight to a target looks flashy, but often, teammates will not be able to fully maximize the damage they deal due to reaction time needed for your move. It can also be difficult to hit since enemies sometimes move in an unpredictable manner. A surer way of hitting Bandage Toss is to walk towards the enemy from the opposite direction of your teammates, preferably after your teammates have engaged the enemy, which places the enemy within striking range for your teammates. Bandage Toss is not cast until Amumu is chasing the enemy unless the enemy and Amumu's teammates are still engaged in battle by the time they are within range. When Amumu is directly behind a fleeing enemy, it is easier to predict their path.
Amumu's Curse of the Sad Mummy, is crucial in team fights and can often be the deciding factor. You should try to have it ready for when a team fight breaks out. Always try to use Curse of the Sad Mummy on as many enemies as possible while your team is in the vicinity.
Amumu's Curse of the Sad Mummy is very effective when combined with many other champions' ultimates, particularly area of effect spells, such as Glacial Storm, Bullet Time, Absolute Zero, Crowstorm and Soul Shackles. Try to coordinate abilities like these to rack up heavy damage at the start of a team fight.
Amumu's Curse of the Sad Mummy can be blocked by Morgana's Black Shield and other crowd control-preventing items/abilities.
Keep in mind that Curse of the Sad Mummy does not stop enemy channeled abilities such as Katarina's Death Lotus or Nunu's Absolute Zero.
If you are running away from an enemy, you can Bandage Toss over a wall to a neutral minion camp to pull yourself over the wall. It's not advised to do this if you cannot survive the aggro from the minions...unless it's been ten seconds since you were hit, and you can steal the enemy's kill by being Executed.
Using Bandage Toss slightly before being knocked back by abilities will first kick Amumu back and then pull him to the target hit.
It is possible to use Tantrum to proxy with Amumu.
Build usage