That's a sample build of Amumu jungler,in my option it's better than the laner because u can gank in every lane and get more kills to be feed and help u team.

In team fights u will use the Bandage Toss in middle of all enemyes and use ur ult to stun all them,use Despair ant Tantrum to lower the enemyes and ur team will kill the other champs.

About the runes,i prefer the defense runes,but if u want u can made the quintesse of experience runes.

I Begin with the cloth armor and 5 potions,then i buy the Mercury's Tread's after that Sunfire Cape,for jungle better and get more kills when u gank.
I buy Aegis of Legion to give armor and magic resist in team fights for my allies,after that i begin my tank build with Force of Nature and Torn Mail,and for last Warmog's to get more life and health regen

Amumu Jungle Pros:
1. U Get More Gold Than in Lane
2. U Get an K/D ratio better.
3. U Get ur build more fast than ur team

Amumu Jungle Cons:
1. If ur team dont have a good solo laner the tower will be lost soon
2. U can be ganked in the begin of the game
3. If u dont gank u can feed the other team trying to gank

I use the Despair and Tantrum to gank and kill the minions in jungle and in my opinion the Bandage Toss is just for stun the enemy,so i put in lvl 5 cuz in lvl 6 i will start my ganks.

The Spells u will use can be the Ghost/Smite or Fortify/Smite,i use Fortify cuz this protect the solo laner when he dies,the ghost is for u can stun ur enemys when they are running and the smite is for an fast jungle.

To Jungle with Amumu u will begin in the Blue Buff,with Despair use one potion to kill him,go to the wolfs and after the Wraiths(if u hav the smite use in the blue Wraith,cuz he heals the reds and hav an attack more strong)then go to the golens and recall.
Buy your Boots(normaly u can't buy the mercury's tread's so u gonna buy the Boots of Speed)
and back to jungle until level 6.Them u will start ganking,remember to always get the blue buff cuz the despair spell use a lot of mana and u cant jungle/gank without mana.