This is my first guide ever. So here it goes...

The jungler. An underrated, yet highly criticized part of every good team composition.
Why is a jungler necessary? More farm for your carries. Easier to gank for said carries. And securing buffs/dragon for your team with smite.

But what makes a jungler good? Almost any champ can clear out the jungle starting out. But the ones that are good at it do it fast, have some kind of distance closer and crowd control. The ones that are great at it also have a bunch of damage output (ie. Nocturne and Lee Sin).

So why is Amumu my favorite?

PROS

Super tanky
Amazing initiator (bandage toss/ultimate)
Great lane ganks
Magic resist shred
Ultimate (it's that important)

CONS

You can (and will) be counter jungled by any other jungler and be killed
Relatively slow jungle
Low damage output
Blue dependent jungle

Marks
I take the Greater Mark of Magic Penetration marks because the little amount of damage that the mummy does do is all magic damage. What else could you possibly get? Nothing.

Seals
For the seals i take Greater Seal of Armor. This is going to help your jungle go smoother. Granted that yes, you get more end-game from per level, but this is going to help you gank earlier. Less damage taken in your first jungle rotation = earlier ganks. So flat armor it is.

Glyphs
For glyphs i take Greater Glyph of Scaling Magic Resist per level. Why not flat MR? Simple, you want magic resist to scale into late game so it's not a main concern of defense stats for you. This should make it so you can rush the sunfire cape and have lots of health and deal much more damage and take more damage. These runes here, are winners.

Quints
Why Greater Quintessence of Scaling Cooldown Reduction? Why not something more useful? These are usefull. 6% cooldown reduction on your ult is a lot considering it's over 100 seconds. Get it. Ult more, win more.

New masteries? OHSHI-

Amumu is a tank.
Think anything different and you're an idiot.
Your damage output is completely based off what you can set up for your carries.

That being said, 0/21/9 masteries are the way to go. Jungling as Amumu you will need the increased duration on the buffs Runic Affinity , so grab that from utility. I find that getting Bladed Armor makes jungling a little faster on him. But i feel that the rest of the mastery points in the defensive tree are self explanatory. Maximize your movement speed when possible in the mastery trees so you can run down any champ and force them to give you a hug.

Bandage Toss
Your ganking tool. Is it what makes the mummy so awesome? Kind of. But that's more so his ult. This skill shot stun the mummy has also pulls you, towards them. Remember that. Make sure you hit them with an auto attack when you have them stunned. You want that MR shred.

Despair
A damage per second ability that's based upon how much health ANYTHING around you has. It's why Amumu can jungle so well. If they get a tard carry that goes atmogs just keep running around them with W up, they'll see W will hit for over 1000.

Tantrum
Reduced physical damage. I tank more.

Curse of the Sad Mummy
Your ultimate. Your game changer. Your escape. Your ability to stop them from getting to your carries. This is why everyone loves an Amumu on their team. An AOE snare. I always am going to auto-lock as Amumu jungle if there's a Morgana, Brand or Fiddle on my team.

With jungling on Amumu you need to take a point in your W first. And everyone at level 2 will put a point into E. Level 3 is where i stray from most builds. Level 3 i start maxing W. I know, you're thinking "WTFLOLBBQ". But i'm thinking faster jungle -> earlier ganks -> my team wins faster. Besides, tantrum is on a cooldown and burns mana much worse than despair. By maxing despair over tantrum, you can just run beside your enemies and chit-chat them to death. And by the time you do your first dragon you would not of had 2-3 points into despair as compared to 5 and would take it down much slower.

SO, skill priority goes Curse of the Sad Mummy> Despair> Tantrum> Bandage Toss.

YOU ARE A JUNGLER! TAKE SMITE OR DO NOT JUNGLE

Seriously, if you jungle and don't take smite, you will get countered so very hard by anyone with a brain. They will ward your dragon, your blue, your everything you ever wanted in SR and smite it away from you. TAKE SMITE.

Flash is completely preference. But it's much more viable on him than most champs since you can flash ult from behind a wall yell "SURPRISE" and your team and you can dance all over their dead bodies all day.

First Items
Cloth Armor and 5 Health Potion to start out.
Not saying this is what i use, but if you're just trying him out, use it first. Then go on to using just a Regrowth Pendant and a health pot. To get an early philosopher's stone. But don't sell the cloth armor or Heart of Gold items right away. You need the cloth armor and you need the heart of gold for Randuin's Omen.

Boots aren't important
But your main concern after the GP10 items and boots after that is health. Grab the Giant's Belt when you can. Then defend this new found health by either getting more armor or more magic resist with Chain Vest or Negatron Cloak. But with the runes you should be able to go for Sunfire Aegis and not worry about MR yet unless your team is feeding their AP carry.

Force of Nature
So after Sunfire Aegis we get Force of Nature. A beautiful combination of items, really. Sunfire Aegis deals constant damage while giving you armor for pesky AD champs, while Force of Nature helps you regen whatever health you maybe missing much faster now that you have lots of health and it keeps those AP carries at bay, too. These two items should make it so you can tank nearly everything.

Randuin's Omen
Next up you're going to want to finish building Randuin's Omen. I don't care how hard their AP carries are hitting at this point in the game, get this next. You will not only have a stun, an AOE snare but you will also have over 200 armor at this point and an AOE slow. They will not run away.

Abyssal Scpeter
Still can't tank everything? Get Abyssal Mask. Great aura for your team, and works even better with your passive. OH, and it gives me AP? Why do i need that? The next item explains why, very well.

WILL OF THE ANCIENTS
Wait...wut? LOLWTFBBQDIX !
I'm not trolling. Get it. You will tank infinitely harder now. With the combination of Abyssal Mask and Will of the Ancients you will over 100 AP on Amumu. Why is 100 an important number? This will raise the damage Despair is doing by a full 1% of the enemies' max health per second. "Big deal, it's 1%." You shut your ***** mouth now and listen. 1% When you're dealing with champs that have 3k health is going to be 30 extra damage per second. But let's do an average, say 2.5k. So 25 extra damage a second. Now factor in 5 champs (125). You are now doing 125 more damage a second to their team. And if your other AP carry gets WOTA too, you will be getting back 50% of the damage you're dealing which should make you an infini-tank.

The only route that works on Amumu is Blue>wolves>wraiths>red>double golems.
But if you know you're going to have a good leash, then you can start at wolves and finish them off before blue even spawns.

So, let's say you're starting at blue. You get a leash and all you do is hit Despair and auto attack the big golem. Make sure to chug a Health Potion once you take damage. Smite when it gets around 450-500 health. Turn off Despair. Get a point in Tantrum.
Move onto wolves. Auto attack the large one. Turn on Despair, Tantrum till they die. Turn off Despair. Although you have blue you should be careful with mana usage. So don't always have Despair up and don't use Tantrum just because you can. It sucks to be at the red camp mana-less and losing health faster than you gain it and you can't even cry anymore.

As a jungler, you should always try to communicate with your team and ping the champ you are going to focus well before you are going to gank. Do not do it 5 seconds before or 10 seconds for that matter. Give your teammates time to prepare. Level 4-5 ganks can fail sometimes though. Make sure you have Flash up just in case. And hit the skill shot Bandage Toss. This will give your lane enough time to spend their cc on whoever it was you decided to hug. But once you get your Curse of the Sad Mummy and the laning phase is still going on. You will always get a kill for your team because of your ult. If not, you tried ganking a lane with Nidalee or Mordekaiser on your team and their Kassadin rift walked to top lane to kill your Irelia. So be ready to blow all your cc on 1 champ if the lane you're ganking doesn't have good crowd control.

I should mention before i get into teamfights that as a jungler you should be warding river like crazy. I don't care if it's the support's job. It's more so your's than anyone else's. You cover more of the map than anyone else. Make it so your team can see all the pretty places you've been too. Be smart with your wards, too. Make sure they cover entrances to river, not just the entrance into bottom/top lane.

Amumu's job in teamfights is to go in, interrupt their team, then die. Don't like dying? Don't play Amumu. Bandage toss whoever you can to get close. Ult if you're pretty close to their carries, or can split 2-3 members of their team apart from each other. You can initiate with a flash ult though. It can be better sometimes since you will have bandage toss up right after ulting and make sure their AD/AP carry can't move.

All in all Amumu is a great team player. Is he the best tank in the game? No. Is he the best jungler in the game? No. Is he the best jungling tank? Yes. I hope you guys enjoyed this or at the very least learned something.