Alright I have been playing Amumu for a while now and I started out laning with him but soon as I started experimenting jungling I found out that jungling was much better and more fun. I find Amumu the best tank in the entire game in my personal opinion but here is what I use when I jungle I usually do very well but since Amumu is a tank he requires a good team in order to win.

Pros
Great Jungler
Farms Easily
Escape Capabilities


Cons
Some Form Of Escape But Not A lot
Common Starting Place For Jungling
Not Alot Of High Damage Output During Ganking

I use the Greater Mark of Health the life added onto with your Quints gives you a substantial amount of life for the easier take down on blue.
For Greater Seal of Armor the magic resistance is good for when your ganking at level 4 and such to endure some of the beating magic users can do while u AoE them down with Despair
For Greater Glyph of Magic Resist since you are jungling and the less damage you take from the minions especially blue golem the better.
For quints Greater Quintessence of Health gives amazing amount of hp just in case you get interrupted while jungling or need a lil extra life for a kill in the beginning.

Cloth Armor and Health Potion x5 are essential just for jungling I have yet to find anything that will work while jungling.
Boots is what I get next after you gank or if none available after full clear of jungle you recall and get Sight Ward x2 for either ward solo top or dragon for enemy jungler or ward bottom if they do not already have one placed.

Mercury's Treads I find these to be the best boots just for the 35% tenacity since you are tanking and need to keep up with them if they CC you so you can AoE them down with Despair

I found that using Aegis of the Legion is very helpful to the team and to yourself giving you a lil bit of everything MR, PR, and HP.

After getting some Advice i was told to adjust some things and i did the adjustments and am rather pleased with the results. instead of gettin Banshee's Veil or Randuin's Omen

I decided to get Shurelya's Battlesong which has some HP and has some CDR for the pestering moment of after a team fight when that lonesome low hp person is running away and you just got the urge to chase him down but ur bandage is on cd =....(

Your next item is either getting Banshee's Veil Or Randuin's Omen all depending on what is hitting you the hardest Randuin's Omen even tho it has a decent amount of health added to it as well as the armor and regen is nice but only If AD Heavy or have alot of CC Banshee's Veil would be a wiser choice for survivability if they have alot of AP.

Abyssal Mask Personally find it the a great combo with Amumu's passive which lowers their MR on hit so stacked with Abyssal Mask means more damage they recieve the ability power helps with ur ability but wasn't really needed in my opinion.

To top the build off instead of having Abyssal Mask you can get a Guardian Angel if you are that pestering little mummy that most likely is turret diving an enemy if they r turret hugging Guardian Angel will save you if turret dive or if you lose a team fight and have a way to escape to survive and defend ur towers from the remaining enemy.




Also if the enemy team is really ad heavy and dont have much AD here is an additional build just in case. Mercury's Treads Aegis of the Legion Shurelya's Battlesong Randuin's Omen Frozen Heart Guardian Angel Or Thornmail if GA Isn't good enough for you picky people =P

If the team is full on ap you can get Mercury's Treads Aegis of the Legion Shurelya's Battlesong Banshee's Veil Force of Nature Guardian Angel .

I always team up Flash with smite just if you need a quick escape or need the extra couple feet to stun with ultimate or bandage.

Teleport is understandable to use if need to spot a player or if allies need assistance or a gank for that matter

Ghost if you prefer ghost more then Flash

The other spells I don't see a reason in using for your a tank that is to soak up the damage and stun them and AoE them as much as possible.

Clarity i find that Amumu does not need clarity for the simple fact of 9 out of 10 he is goin to have blue buff and not have to worry about

Clairvoyance is something a support should have not a jungler

Exhaust you are amumu a tank not someone who is suppose to suppress someone from doing damage that is someone elses job also ur not suppose to 1v1 ppl

Cleanse you are a tank and do not have to worry about being cced since you are amumu the mightiest tank there is and have 35% tenacity as it is with Mercury's Treads

Fortify Something i have not seen a amumu with fortify and jungling at same time

Ignite Your a tank your not suppose to be getting kills or finishing off champs with ignite

Heal If your are having to use heal tin order to survive then something is wrong for that is got to be alot of damage

Rally gives damage and life yet doesnt give enough to be considering a good thing to use on Amumu imo

Revive that was a level 1 summoner spell to use back in the day you shouldn't ever have to use Revive and you are also a tank why would you be using Revive to save a turret or something?

When jungling with Amumu you of course start at blue hopefully with a leash of course and soon as they leash or if no you hit Despair and start auto attackin the big golem hit Health Potion soon as u take damage when the golem gets down to about 440 hp smite the big golem and kill the lil guys

Move on to wolfs you should have after killin the two lil guys hit lvl 2 and put that point in Tantrum after that hit another Health Potion and us Despair and Tantrum to kill the big wolf first then kill small wolfs

Then move on to wraiths you us Health Potion and use Despair and Tantrum and auto attack to kill the blue wraith first the others should die at exact same time if not pretty close to each other after that you should hit lvl 3 put that point in Despair

Now you have a choice of goin to either 2 golems or red buff i usually go for red buff now for this one you should wait till at least ur mana is at 160 before initiating use ur Health Potion and use Despair and Tantrum to auto attack the red lizard to about 500 life if not a lil above about 520 or so smite and move on to the golems and finish them off then you can either gank if available or recall get ur stuff and go jungle some more gettin their blue buff if they dont have a jungler or gank or farm some more starting at wolfs again.

What has saved my life more then anything else that i can think of when u ever run into a bush or anywhere at wrong time you can Bandage Toss to a enemy minion or neutral minion in the jungle and escape you can fly through walls when you Bandage Toss it can take some practice and not always works but when it does it is amazing lol

Bandage Toss Throws a bandage to a target location. If it hits an enemy unit, Amumu will pull himself to the enemy, stun them, and deal 80/140/200/260/320 (+100% of ability power) magic damage.

This is a skill shot that is like Dr. Mundo , Lux , Morgana , Ezreal but what you aim to do is aim ahead of the person if a minion is not in the way of course lol but there is a slight delay in the bandage for it has to travel that distance unless the target is standing still and you are in a bush

Despair Toggle: nearby enemies take 8/12/16/20/24 magic damage plus 1.5/1.8/2.1/2.4/2.7(+1 of ability power)% of their maximum health each second.

You get surrounded by wat appears to be tears falling from his eyes in a big puddle around him doin a AoE damage that ppl take damage while they r in the puddle great thing about this ability is it does percentage of their life instead of a specific amount of damage.

Tantrum Passive: Amumu takes 2/4/6/8/10 reduced damage from physical attacks.
Active: Amumu deals 75/100/125/150/175(+50% ability power) magic damage to surrounding units. Each time Amumu is hit, the cooldown on Tantrum is reduced by 0.5 seconds.

This is Amumu's AoE that is majority his farming specialty for every minion that hits him his CD is reduced on tantrum so you can farm minions alot.

Curse of the Sad Mummy Amumu entangles surrounding enemy units, causing them to unable to attack or move for 2.5 seconds, dealing 50/100/150(+35% of ability power) magic damage to them for each second

This is Amumu's unique amazing ult it is the best in the game imo out of the tanks you can not find a better one you move to group up the enemy and u stun all of them so you team can go in and slaughter the enemy team for like Katarina her ult combined is deadly with Amumu's Ult

Amumu is nothing without his team if he has a bad team then Amumu can not carry his team he doesn't throw out that amount of damage to carry the team. Amumu combined with a team like Katarina Nunu & Willump Morgana Rumble etc etc...

Ad wise to go with Amumu's stun you can have like Jax [Tryndamere]] Xin Zhao Twisted Fate etc etc...

But Basically Amumu is nothing without his team this is League Of Legends a team game.

Also On Amumu's Bandage Toss you can use it to stun a enemy if they r chasing, pursueing, or attacking one of your carries or support units that r low life or just need to b saved in general you can bandage toss to save them from the enemy so ur team mate can get away and live.

This was my first build and open to any advice or something. Amumu is a wonderful tank and i have a blast just playing him seeing him fly from a bush or somethin using Bandage Toss to gank someone or escape as well as Amumu having the best Ultimate in the game in my opinion an AoE stun that does a decent amount of damage included.