To be honest I have no idea how to actually make a guide so bear with me. However that aside the method of jungling Amumu in this guide has been proven to work. The build in this guide is for a tanky AP Amumu with perhaps more AP than normal early game. You wont find any nice pictures of items etc in this guide as to be honest I'm largely incapable of such thing. However don't let that persuade you not to read this guide. If you use my masteries and runes I'm sure any competent player will find success if they use the items I suggest as a guide of the kind of items you should buy to become, I would argue the best champion choice for any 5s team. It seems everything I really want to say is covered in later sections so I will be brief here.

For Runes I find Marks are best as Magic Pen, to be honest there arn't really that many options for Marks on Amumu and the Magic Pen runes do nicely.

Armour seals are simply a must if you wish to jungle, Amumu simply jungles on too low health otherwise. They also make you fairly survivable really game and help escaping an aggressive counter jungle. Amumu effectively dies to all other jungler unfortunately.

I go for the AP/18 Glyphs but flat MR is also acceptable. The AP/18 gives a big boost to your W and E mid game.

There are many ways you could go with Quints but I find the Flat AP gives you a faster jungle and makes you dangerous with early ganks. Armour Quints are a good alternative

The defensive tree speaks for itself really. Perhaps the only oddity is the fact there are no points in the MS however they are sacrificed for the damage block and the hit-points regen which are crucial for my jungle path.

The final 9 points are really more up to preference. I would argue the 4 AP 4% cooldown reduction and Magic Pen are more beneficial than anything in the utility tree however.

Pros

Outrageously Strong Late Game
Game changing Ult
Fast Jungler
Relatively unexpected build

Cons

Needs first blue majorly
Relatively weak early, average mid
Jungles on really low health if you follow my path
Can be counter jungled (Though its not a huge deal unless they find you)
Somewhat farm dependent

I'm afraid no one will read this guide because I don't have any item pictures etc but I hope its not so. In any case I will do my best to keep it interesting. For starters the Items part of any guide is always going to be a little ambiguous as items are directly linked to play-style and thus without my play-style these items wont really be of optimal use. However hopefully the runes/masteries give you some idea of the role in the team and the ways in which you should play with the items. The Items at the start of the build are ideal, but most games will require you you to buy slightly different items to fit the cog you play in teamfights. I dont know how to make the item progression above look so that you know the exact progression i.e selling items etc but to be honest its somewhat game dependent. So really after a while playing an Amumu of this type you will know what is a slightly better variation based on the specific enemies/allies and the way the game is going.

Start with boots and 3 potions. Depending on the damage done to blue you can jungle to the point you return to base and buy a dorans ring and many potions as you need the health potions. You can't really gank with this build before 4 and even then if they have flash you are relatively unlikely to get a kill. This is the nature of early game Amumu. After your first dorans ring I usually follow up with a second for the mana regen as you really do just spam in jungle, it also gives you good AP and health.

After this it will really depend. If you have not died which is likely and got a kill at least when you hit 6, which is also likely I find it is good to go Rylais getting the health first. If all goes well finish it, if you need more tank based on the game go for a 700 armor. After this Frozen heart is ideal for the CD reduction, mana and armor. It is a good item. Many Amumu players I see to Sunfire which I think is majorly over-rated. The passive is just average and not worthy of your money. Upgrading your boots is costly and very dependent on the game so it is best left up to your discretion to be honest, but if you follow this guide you will learn when to with time.

If you get Sorcerers Boots Rylais and FH you will do a large amount of damage, especailly over time. You will be able to destroy adc in seconds as your AP will be suprisingly high from your masteries/runes and items. After these Items Abyssal Scepter is ideal for your low MR and gives a good passive and more AP. This all really is game dependent but at this point you really do fill a massive part of a team with your tank and damage. More than any other champ with items of a similar cost, I would argue but it is not something I can really prove to you. Anyway. From here Rabadons will make you a complete beast. You will one shot adc and melt tanks with your W. Spamming E will wreck almost anything. Randuins is also a good choice for the health, armor and teamfight active.

Speaks for themselves

Again skills sequence is game dependent. However always get W first followed by E. Some people will say get Q third so you can gank but to be honest unless the lane is pushed, which is unusual go E third for faster jungle and go Q fourth. After this it really is game dependent. Going points in E early seems best to me, and to everyone I have ever seen play high elo games. It simply is the best. Q and W however is more of a debate however. Q has such a high cooldown that maxing it early seems to me misguided as even if it has a low cooldown it is not low enough to be that useful as team fights are comparatively rare early and you will not use it twice in a gank unless they are massively overextending. W better to get than Q for that reason as it gives very good damage even if not instantly noticeable. If the team is full of squishy champs Q is more viable before W but in my experience W is more important.

Depends on how much help you get on leash, but if you get for whatever reason more help with blue. This is far more likely playing top right as the adc can get a few shots etc. If this happens you can go blue, wolves, wraiths, red, wolves, wraiths. You recall but a dorans ring and potions. Ganking is relatively rare and ultimately not worth your time in first path due to the loss of gold and experience you face vs the chance of success. You can really only gank mid I would almost argue. Anyting else is almost never worth it in my experience.

You are likely the tankiest member of your team at all times except early when perhaps your top might be. Your role is tank, but you are not a straight tank, you cannot take big damage until you get some armor and health. That is why I suggest Rylais and FH as your first items other than boots. However both items give you damage in the form of CD reduction and AP. Thus you become an AP Tank. You should either initiate or initiate second very fast to try catch more of their team as they will likely naturally try focus the first person. Your ult is ridiculous, especially. with some AP. it stacks 1 to 1 just like your grab. After your ult the state of the fight will dictate what you do but really you are a team fight hero as your ult illustrates. If you lose a fight but you catch many people in your ult on good initiation your team cannot ask anymore. If you ult 4 and you lose the fight essentially your team is bad. It happens.

Though this is the summary there is so much more I want to say, and things I can't really describe in words in terms of game-play. However if there is no thing to be noted Amumu is not at all a early game champ. He scales very well into the late game however. Teammates may often do not realize this however. They may ask for ganks that they dont really need and set you back. Too many players do not think of jungle as a lane which needs to be maximized for gold and experience and rather think of you as someone that just exists to help them in lane by ganking. This often happens if they are losing their lane through lack of skill. Try help them out by let them know late game you will scale massively in the late game. Most people do not know he has two abilities that scale 1 to 1 with AP, one that scales half but can have effectively no CD and AoE that can do something like 8% of maximum health per second with full items. You are simply a beast late game.

Do try this build and give it time like anything else. Amumu is so much more fun than most champs due to his unique skill set. Jungle really gives you the freedom to be creative rather than boring lane meta. Don't knock it until you try it. If this build doesn't work for you just give it and Amumu time and it will work.

Many people may doubt you in game but then shut up when you dominate. especially when your build is boots 2 dorans they might flame but if you watch high elo games it is common. just tell them that. Some might flame you for not ganking till 4 or 5 and say you should get Q at 2 or something equally ******ed. Amumu just doesn't to early game as well as some jungles. Its a trade off for late mid/late game some people simply can't understand.

Ive never made a guide so I don't really know what to expect. It's clearly not well made, essentially 2 hours work but anyone who is any good at lol will I promise succeed with this build with a little work. I would show a screen shot of like 7/8 wins but I don't know how.