In this build you will be the center of attention because you will kill everything that is not your teammate and moves. This build requires a lot of skill and practice. Try Amumu out first because i dont want you to down rate because of your lack of preparation and recklessness. -_-
Also please tell me why you down rate it.

Pretty self explanatory. Mark of Insight is for pure offense and will make a BIG difference. I get Seal of Clarity because I never run out of mana. Glyph of Celerity is to me better than Glyph of Focus because when you level up Tantrum you also get a small cooldown reduction boost and it will make a great difference in battle. You can keep up the cost because of the mana regen.

Offense Tree -
Archmage's Savvy: AP it gives a small boost that can make a whopping difference
Deadliness: Its makes a small difference but the other skills will use summoner spells that you will not use.
Sorcery: Eh you know what it is!
Archaic Knowledge: By far the best skill for mages only rivaled by maybe havoc which is the at the end so we will go with this.

Defense Tree-.
Sorry but you are already tanky and to much tankyness will not do you good.

Utility Tree-
Spatial Accuracy: For teleport.
Perseverance: Health and Mana Regen a must get for this build.
Expanded Mind: For extra mana
Meditation: Mana Regen
Utility Master: In 5v5 you are advised to farm the Blue Golem.
Quickness: I find that most Amumu players that dont have quickness have trouble chasing after double stun.
Blink of An Eye: For flash but they say they re going to get rid of it so if they do advise getting Ghost.
Intelligence: Cooldown reduction goes a long way with Amumu.
Presence of Teh Master: I think that this is probably a little lame but nevertheless useful.

Note: If you are not level 30 yet than i recommend completing the offense tree first rather then the Utility.

Regrowth Pendant is a fine choice as for survivability and it can be later be built in to a must have item Phil's Stone. The possible alternative are Doran's Shield (although you cannot build it in to the Stone) but NEVER Doran's Ring since the AP is not enough for First Blood and the mana regen is just to small. I have seen many newbish Amumu characters make this common mistake.

Boots are almost the second item for every build. This is dependent on what are you fighting. Most are DPS? Use Ninja Tabi. Most are CC? Use Mercury. Both? I advise you to use Mercury since this build needs a bot MR but it is you decision.

Sunfire Cape is a Must-Have because of the AoE damage and the tankiness in the item.

Abyssal Staff is almost used in every build considering Amumu because of its MR, AP, and its aura that stacks up to Amumu's passive.

Rylai's Slowing Tears are awesome and the stats are good for tanks .

Zhonya's Hourglass may seem a bit weird to you but you can tower dive pop it and come out safely or at least alive. Also you can activate Despair go near to your enemies and with your Sunfire pop it and deal a bit dmage befor YOU'RE hurt.

Last Item: I'll let you'll chose on that one as it depends. If there is nothing that is a major problem I recommend Guardian Angel because you might want to tank towers at this late game.

(Passive): Amumu takes reduced damage from physical attacks. Each time Amumu is hit, the cooldown on Tantrum is reduced by half a second.

(Active): Amumu deals magic damage to surrounding units.
Your highest damage skill and your most costing one as well. The damage reduction is small but makes a difference. If Amumu is hit the cooldown is reduced so you'll be able to spam a whole lot.


Toggle: Overcome by anguish, nearby enemies lose a percentage of their maximum health plus base damage each second.
An AoE damage skill that deals flat damage and scaling damage. It might deal more damage to tanks but the flat damage makes it more useful taking out pesky carries.


(Active): Amumu tosses a sticky bandage to a target location, stunning and dealing magic damage to the first target it connects to while he pulls himself to them.
Your chasing skill. You can use this to juke and it is a great opener. The stun duration and the area stay the same so we will be leveling this one at the end.


(Active): Amumu entangles surrounding enemy units in bandages, dealing magic damage and rendering them unable to attack or move for 2 seconds.
This is your secondary chasing skill, your primary defense skill, and your awesome ultimate. This can stun while letting your teammates attack and letting you escape or dish some damage.

It is best to max out tantrum first as the minions can deal little to none which makes him a very good farmer.
Next is Despair since it is a good combo with the Hourglass and can quickly kill your opponent in 20 seconds.
Bandage Toss is a high damage skill that has the same stun duration and length at every level so it will be best to max this last.
Curse Of The Sad Mummy is a stun that causes a lot of rage when you are AP amumu.

Teleport is just so you can get back in to action. If you have a Teemo on your team you can teleport using via mushroom.

Flash is just to get a better position for your ultimate. It can put and/or gain a little distance from your enemies.
SUBSTITUTES

You can also run through enemies making this very good juking skill

A defensive and offensive skill. It also has a place in the offensive tree so in can replace deadliness.

All the others are not important enough to replace the skills already listed.

Pros:
*Can score an ace by himself
*Can be qualified as a bruiser
*Not very item dependent
*Has good juking skills
*Two survival buttons"
*High AoE Damage"
*Has a bit attack damage at the end
Cons:
*Has below average stats for a tank
*Unlikely to get first blood
*Has to get close to be effective (although I can rule this out with Bandage Toss)
*Has a hard to get skill shot that requires a whole lot of practice"


" " Means most important

Maximizing Tantrum can cause the minions to do 0 damage because of the Passive making him an awesome farmer. Get the Blue Golem since you can pop Despair and let it on and on... Get the drag to get a bit of gold.

I'm going to show you how to juke or at least the best i can without showing a video. If someone is out to get you and you know you are going to die, there are three possible ways to get out. One is run but in most cases it doesn't work so it is better to juke or put on a show.

If you are being chase in the jungle you can bandage toss your opponent and flash behind their back. You can also use your ultimate bandage toss to a nearby creep or minion. You can also flash into range and bandage toss a nearby minion. You could just go old school and use your walking the other way when approaching the bush skills!

!Remember that putting on a show can be better than technique If you know a juking move that isn't effective but dazzling it can cuse your opponent to say "WUT?" and they won't register what happened. This however depends on the person, if they have quick reflexes they can foil it easily tho.!

I get it purely for the armor and AP. The Ability is an added bonus. The ability it gives you is that you get to be invincible but cannot take any actions for 2 secs. Why it is so important it is important is that you can turn on despair use zhonya and the despair aura is still active.
The 2 second is also to let your tantrum cooldown. So basically you can just pop on despair run in to a crowd, use tantrum, press 5, press tantrum again, and watch them flee.

Harrassing:
If you have Golem's you can turn on despair and harrass everyone on your lane and spam E E E E!!!
Farming:
You can stand in front a large lane full of minions and get out unhurt because I've seen when
minions can't hurt Amumu (super minions exc.). This makes him a great farmer.
Fighting while low HP:
You will be amazed how much damage you can take and deal. Especially with 2 stun skills you can easily dispatch a fragile carry.
The skill shot:
Probably the hardest skill shot to manage as it has to get close if the target is moving. The skill shot does not move if YOU move. You also have to calculate the movement and the target can run in to his/her tower and use a CC on you.