Firstly, because he has reeeeealy nice damage in teamfights plus his passive, which reduces his terget's magic resist with his basic attacks.
Secondly, he is even better in 1v1 as he is not a full tank, he has damage AND spell vamp.
Lastly, i like playing him AP :)


Pros:-Nice cc Cons:-His skillshot needs some practice
-Still tanky even if you build AP -Cries A lot

Classic runes for mages.

REDS:magic penetration
YELLOWS:mana regeneration
BLUES:ability power
PURPLES:flat ability power

Well, in masteries I go 21/0/9.

OFFENSE

:ability power, cooldown reduction, magic penetration, ability power per level, increased damage dealt, bonus ability power and bonus damage to targets below 40% health.

UTILITY

:mana per level, reduced recall time, movement speed and bonus buff duration.

Start with boots of speed and 3 health pots.
In early game you should have hextech revolver, boots of speed and catalyst the protector.
Later you should go for will of the ancients, sorcerer's shoes and rod of ages.
Then buy rabadon's deathhcap and void staff and finally rylai's crystal scepter.
Also great items are abyssal scepter, morello's evil tome, deathfire grasp(awesome with all the ap champions), zhonya's hourglass and (haven't tried it yet) lich bane.

Bandage Toss - Amumu tosses a sticky bandage at a target, stunning and damaging the target while he pulls himself to them.
Throws a bandage to target location. If it hits an enemy unit, Amumu will pull himself to the enemy, stun them, and deal 80/140/200/260/320 (+1) magic damage.

Cost
80/90/100/110/120 Mana
Range
1100

Great ability to initiate in teamfights and evading yourself from your chasers in the jungle, even when you are tower-diving.

Despair - Overcome by anguish, nearby enemies lose a percentage of their maximum health each second.
Toggle: Nearby enemies take 8/12/16/20/24 magic damage plus 1.5/1.8/2.1/2.4/2.7 (+0.01)% of their maximum health each second.

Cost
8 Mana per Second
Range
0

Quite good ability for the enemies who have bought a lot of health.

Tantrum - Permamently reduces the physical damage Amumu would take. Amumu can unleash his rage, dealing damage to surrounding enemies. Each time Amumu is hit, the cooldown on tantrum is reduced by 0.5 seconds.
Passive: Amumu takes 2/4/6/8/10 reduced damage from physical attacks.

Active: Amumu deals 75/100/125/150/175 (+0.5) magic damage to surrounding units. Each time Amumu is hit, the cooldown on Tantrum is reduced by 0.5 seconds.

Cost
50 Mana
Range
400

Very useful ability if you are building AP.

Curse of the Sad Mummy - Amumu entangles surrounding enemy units in bandages, damaging them and rendering them unable to attack or move.
Amumu entangles surrounding enemy units, dealing 150/250/350 (+1) magic damage and preventing attacks and movement for 2 seconds.

Cost
100/150/200 Mana
Range
600

One of the best AOE ults and ver useful in teamfights.

Cursed Touch - Amumu's attacks reduce the target's Magic Resistance for a short duration.

Useful passive if you have some AP in your team.

I suggestFlash/ Ignite as your spells but here are some alternatives:

Ghost:Quite good alternative for your Flash

Well, if you have a 3v3 premade team you should have someone else who has really nice combos with amumu. But if you don't have, then you will have some problems as amumu is a really teammates-dependent champion.

So, this was my first "full" guide (i believe) and i hope you liked it. I will write description in my other guides too when i finish with my exams