Health, Health Regen.
Mana, Mana Regen.
Range
Ability Power
Attack Damage
Attack Speed
Armor
Magic Resist.
Movement Speed

Like most junglers Amumu starts with a cloth armor and 5 health potions. When jungling Amumu you should always start at the blue buff. It is well known that Amumu starts there so you should always ask your team to protect the blue buff and have someone leash that way if the enemy team attempts a gank you will see it coming and be able to flee or if your whole team is there fight back.
Jungling Sequence:
1.Blue Buff
2.Wolves
3.Wraiths
4.Red Buff
5.Golems
6.Wraiths
7.Wolves
8.Gank Top/Mid/Bottom Lane

From there on you can either keep ganking, steal the enemies jungle, or keep using your own jungle and kill the camps as you go by.

Health: 472(+84 per level)
Health Regen.: 7.45(+0.85 per level)
Mana: 220(+40 per level)
Mana Regen.: 6.50(+0.525 per level)
Range: 125
Attack Damage: 47(+3.8 per level)
Attack Speed: 0.638(+2.18% per level)
Armor: 18(+3.3 per level)
Magic Resist.: 30(+0 per level)
Movement Speed: 310

Health: 4255.66
Health Regen.: 130.64481
Mana: 940
Mana Regen.: 15.95
Range: 125
Attack Damage: 115
Attack Speed: 0.874
Armor: 338.22
Magic Resist.: 211
Movement Speed: 411

Passive(Cursed Touch): (Innate)Amumu's autoattacks reduce the target's magic resistance by 15 / 25 / 35 for 4 seconds. The debuff doesn't stack but it refreshes with every autoattack.

Q(Bandage Toss): (Activate)Amumu tosses a sticky bandage in a straight line. If it contacts an enemy, Amumu will pull himself to it, dealing magic damage and stunning the target for 1 second.
Range: 1,100
Leveling Up: Mana Cost: 80/90/100/110/120
Cooldown: 16/14/12/10/8
Magic Damage: 80/140/200/240/280(+1.0 per ability power)

W(Despair): (Toggle)While toggled on, Amumu will be surrounded by a small damaging area of tears. Enemies in the area will be dealt a percentage of their maximum health plus a base amount as magic damage each second.
Mana Cost: 8 per second
Cooldown: 1 second
Radius of AoE: 300
Leveling Up: Base Magic Damage: 8/12/26/20/24
Max Health To Damage Ratio: 1.5/1.8/2.1/2.4/2.7%(+0.005 per ability power)

E(Tantrum): (Passive)Amumu takes reduced physical damage from autoattacks and abilities.
(Active)Amumu will make an instantaneous tantrum, dealing magic damage to surrounding units. Additionally, each time Amumu is hit by an autoattack the cooldown on Tantrum's active will be reduced by 0.5 seconds.
Mana Cost: 50
Radius of AoE: 200
Leveling Up: Physical Damage Reduction: 2/4/6/8/10
Cooldown: 10/9/8/7/6
Magic Damage: 75/100/125/150/175(+0.5 per ability power)

R(Curse of the Sad Mummy): (Active)Amumu entangles surrounding enemy units, dealing magic damage and rendering them unable to move or use autoattack for 2 seconds.
Radius of AoE: 600
Leveling Up: Mana Cost: 100/150/200
Cooldown: 170/150/130
Magic Damage: 150/250/350(+1.0 per ability power)

When jungling Amumu you always want to start with his W(Despair) because it does flat damage plus a percent of the target's health and its a crowd control that can be turned on and off. Next you will want to get a point on his E(Tantrum) because it is also a crowd control and has a short cooldown and the cooldown lowers every time you are hit by an auto-attack which is great for jungling. on reaching level 3 you will want to upgrade despair again so you can kill jungle creeps a bit faster, or if you want to gank right away upgrade your Q(Bandage Toss) on reaching level 3. i prefer to get Bandage Toss at level 4 because I'm usually level higher than the enemy team and I want an advantage when ganking. Upon reaching level 6 upgrade Amumu's R(The Curse of the Sad Mummy)for obvious reasons. The rest is pretty much get Deaspair full level first. Next Tantrum then at last you want Bandage Toss.

First of all I would like to say that the build for this guide is build that I use pretty much all of the time. For me it works great and I know some people probably prefer a Frozen Heart over Thornmail, so I will be creating a list of substitutable items at the end of this build and I will also have a description saying when it is a good idea to change them. For example I had a game where the entire enemy team were ranged dps (all with serge) and what I ended up doing was go completely off this build and got only armor items and because of that they tried to 5v1 me but i was untouchable and they were all underlevelded for pushing mid at the begining for like 5 minutes.
Substutable Items for...
Mercury Treads-Boots of Swiftness(For when you prefer to be able to catch up to enemies you are chasing)
Mercury Treads-Ninja Tabi(For when you feel you need that extra armor and the passive to reduce the damage dealt by auto attacks)
Thornmail-Frozen Heart(For if you want more mana and cooldown reduction)
Sunfire Cape-Frozen Heart(For when you dont want the extra health and want more armor, also if you want to keep the Thornamil and get the Frozen Heart too)
Sunfire Cape-Warmog's Armor(For when you dont want the extra armor and want more health)

I will be making new chapters for runes masteries ect. So I would appreciate if viewers didn't vote for what is currently in the build. Also please leave comments and concerns about this build thanks.

http://leagueoflegends.wikia.com/wiki/Amumu(Stats/Skills)