Ammumu is a jungler with high jungle sustain and very strong ganks. His Tantrum and Despair allows him to clear the jungle really fast. And Curse of the Sad Mummy is arguably the strongest Crowd Control in the whole game. Ammumu is a really strong initiator and a really solid jungler that's why he is such a strong pick in ranked games and can easily turn the tides of the battle into ammumu's favor.
A special shout out to LeChuaf900, now you suck even more!

Perhaps one of the oddest champions in the League of Legends is the Yordle known as Amumu. His life before joining the League remains unknown... especially to Amumu. All he remembers is that he woke up alone inside a pyramid within the Shurima Desert. He was entwined in mummy wrappings and he could not feel his heart beat. Furthermore, he felt a deep sadness that he could not entirely explain; he knew he missed his parents, though he could not remember who they were. Dropping to his knees, Amumu wept into his bandages. No matter what he did, it seemed he could never stop his tears or sadness. Eventually he stood up, determined to wander the world to discover his past. Amumu traveled all across southern Valoran - a feat that is not easily dismissed.
While Amumu still hasn't learned much about his past, he has learned a great deal about who he has become. He is most assuredly undead, though he harbors none of the evil characteristics typical of undead beings. He also seems to keep trouble at arm's length; Amumu was able to traverse all of Southern Valoran without so much as a single bad thing happening to him. He was just sad, and the people and beings he encountered eventually shared his sadness. Ultimately, he made his way north across the Great Barrier to the Institute of War, the home of the League. Amumu's story was compelling to the summoners he met there, and they invited him to take part in a League Judgment. His success within the League as a champion has given Amumu something he desired: a home. With his present (un)life secured, he now hopes the friends he has made will help him discover his past.

Pros:
Strong jungler
Good sustain in the jungle.
Good AP ratios.
Low skillcap.
OP Bandage Toss
OP Curse of the Sad Mummy

Cons:
Get's poked down at mid quite easily early on.
Might be a little hard to lanes Bandage Toss.
Not ranged.
Mana runs out fast sometimes.

This passive works really well with Abyssal Mask when midding and when playing as a jungler, it makes ganking mid so much easier.(Well, generally it helps in other lanes too but at mid it helps more as reducing the enemy's magic resist not only boosts your damage but also your AP Carry's.) Does not stack but refreshes the duration. Can't be blocked by spell shields or Black Shield.
Your Bandage Toss is your initiation tool. It helps you get into the middle of your enemy team then follow up with Curse of the Sad Mummy.Procs spell vamp and the slow from Rylai's Crystal Scepter.
This is your source of sustain damage. This skill grants you the ability to shred enemy tanks. When you are playing as a tank nobody will target you and you will constantly be able to do % of enemy's max health as damage. Despair procs spell vamp and the slow from Rylai's Crystal Scepter but with diminished affect. Despair damages Black Shield and does not affect spell shield.
Surprisingly even if you play Amumu as a tank, Tantrum still have quite a lot of burst. On the other hand, if played AP there will be a massive amout of burst. Tantrum procs spell vamp and the slow from [Rylai's Crystal Scepter]]. Tantrum pops spell shield and damages Black Shield.
This is basically what ammumu is all about. A massive aoe stun that prevent them from doing anything for 2 seconds. This can change to tides of battle easily to your favor. Use it well, win the game. Curse of the Sad Mummy procs spell vamp and the slow from Rylai's Crystal Scepter. Curse of the Sad Mummy pops spell shield and damages Black Shield but entangle is negated.

I max this for both the builds especially at jungling you need your Tantrum for the ruduced damage you take and the strong aoe damage to clear the blue golem fast. While laning at mid consider taking Bandage Toss first if your team decides too stick together and invade.
Max cuse of the sad mummy whenever possible because that is the strongest ability in your kit and the most useful one too.
Max Tantrum next as the reduced damage is effective against jungle creep, enermy auto attack poke and minions. The ability itself scales off 50% AP which is the ability that's the easiest to land and with a high amount of damage.
Max Despair after that as it deals aoe damage and helps burn down your enemy's health. It scales well with your AP.
Max Bandage Toss last as it is simply a tool for initiation unless you can make sure you land all your Bandage Toss on your enemy carries.

Start at wolf camp. Get a leash and use Tantrum to kill it quick. Make sure you start killing the Big wolf first.
Next go over to the Ancient Golem and wait for your Solo Mid to attack the Ancient Golem first then double Smite the Ancient Golem and finish up the two lizards. Up your Despair.
Next go to wraith clear it by spamming your skills.
Go to double golems.Spam skills.
By now your smite should have come off cooldown. Start red at when it's at about 1000hp, double Smite it.Up your Bandage Toss. After this you may want to gank or if not, recall pick up Regrowth Pendant for your Philosopher's Stone. It should be around 3-4 minutes now, head to the dragon and Smite the dragon 7 times and earn around 1k global gold for you team. After this recall then gank or continue jungling.

As a Jungler there's no way to miss a last hit in the jungle.
As a Solo Mid you should not have problems last hitting as Amumu's attack animation is really fast. You should always aim to have 100CS by 10 minutes. At around level 6,go to the center of the minion wave use Tantrum and activate Despair. Immediately deactivate once the minions have all died. When your wave is pushed up, go take the wraiths. Take the wolves too if possible. This way you would be constantly ahead in CS.

As a jungler,run up to the enemy team, Bandage Toss followed by Curse of the Sad Mummy then Despair and Tantrum. As a AP Carry, wait for your tank to initiate then immediately Bandage Toss then Curse of the Sad Mummy use Despair and Tantrum. After your burst stay back and wait for cooldowns to refresh.

Summoners Spell
This summoner spell works so well on Amumu, it lwt's you quickly flash+ Bandage Toss to engage or Flash away to safety.
You are a jungler. Enough said.

Runes
Greater Quintessence of Movement Speed for helping you engage or escape.
Greater Seal of Armor for helping to keep your health relatively high while jungling early on and tanking AD damage at late game.
Greater Glyph of Magic Resist for tanking during the late game.
Greater Mark of Magic Penetration for destroying your enemy's defenses so you can actually deal some damage to them.

Items
Mercury's Treads Helps you reduce the amount of CC you take. Very useful.
Aegis of the Legion Helps you tank and it makes your team slightly more tanky too.
Frozen Heart Anti AD Carry item.
Shurelya's Battlesong Helps your team quickly initiate or disengage.
warmorg's armor This item will turn you into a unkillable tank.
Randuin's Omen The unique active helps your team secure kills and it gives a nice amount of health and you know you can escape anyone with this item.

Masteries 0/21/9
Standard tank masteries with pioints into more movement speed for engaging.

Summoner Spell
This spell is a must, for escape and for engaging.
ignite size-20 This spell helps you secure kills and increase your AD and AP.

Runes
These are standard solo mid runes.

Items
This increase your burst damage and increase tankyness while reducing your enemy's magic resist.
Makes you more tanky and gives you damage.
THis item is a MUST take for AP Carries.
More health, more AP and a noticeable slow.
This item just give you all the burst you need to instantly melt your enemy carries.

Masteries:
21/0/9
AP in offensive tree and some mana and movement speed.

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Thanks for reading!

By now you should realise this is not like my 1st troll guide. This is actually a serious guide.
http://www.mobafire.com/league-of-legends/build/zilean-solo-mid-support-262553