Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Please allow me to introduce my favorite champion in League, Amumu. I absolutely adore this little guy. He's so tiny, and cute, and sad, that you just want to pick him up and cuddle him forever. But if you know anything about Amumu and are on the enemy team... run. Run as fast as you can. Amumu has spent millennia upon millennia suffering, alone, and tormented. And he's going to take it out on you.
Some people will argue that Amumu should have more defensive runes, or something that can help him sustain fights longer. These people don't know Amumu too well. If you go and actually read your Despair ability, the percentage of life lost does scale every 100 ability power you have. So the more AP you have, the higher the percentage. This will will be covered a little more in Items and Skill Sequence.
I have seen a lot of Amumu players fail, simply because of their builds. Some people look for the wrong kind of build. Amumu is actually a tank, but that does not mean he needs to build completely defensive related items. You have to take your spells into consideration, do some math, and then "facepalm" when you realize what was wrong. To start, you absolutely need to get your Sunfire Cape online as fast as you can. Do NOT gank or get caught out without it. This will provide you with some defense for camps, and the tick damage will help you clear so much faster. It also provides some defense if you get caught out by another physical jungler. Once you get your Sunfire Cape and boots online, you should also have your ult, Curse Of The Sad Mummy as well. It is officially safe to gank. With your cape and boots online, you should also be able to travel into the enemy jungle to start stealing their camps. This will help slow down their jungler, which is exceptionally important. But don't forget to ward as much as possible to keep eyes on everything. Now we get into where Amumu really shines. Rylai's Crystal Scepter and Liandry's Torment. Your W, Despair, is a constant. As long as you have mana, your Despair is ticking. So combine that with Rylai's and you now have a permanent slow to any champ without an escape. Now read Liandry's. 1% health every .5 seconds, doubled to 2% every .5 seconds against movement impaired enemies. That affects your Bandage Toss, the slow from Rylai's, and your ult. Now add in Amumu's Despair (keep in mind the ability power scaling the percentage of health lost, which should be 7-8% per second regardless of defenses). And then add in the 43 damage at max level from Sunfire. You can do no less than 12% of a champion's health per second just by sticking to them. Throw in an ult and a couple Tantrums... and you can shred absolutely any champion in game regardless of their protections. This is particularly useful against champions like Mundo with ridiculous health and healing. And if you somehow manage to get caught out alone, and get cc locked, make sure you hit your Despair. Even if they kill you, you are still going to do a crazy amount of damage to them, maybe kill one or two, but definitely forcing them to back, which gives your team time to advance, or clean up any mess they may have themselves in.
One major issue I've noticed on a lot of Amumu junglers, is that they start the match with their W, Despair, thinking its going to tick everything down. Read your E, Tantrum. Every time Amumu takes physical damage, it lowers the cooldown of Tantrum. This is your go to ability on all jungle camps. Even if you are low on mana, but don't want to back just yet. You can continue on with just your Tantrum ability and basics. Level your E, Tantrum for jungle camps. And level your W, Despair, to help with camps, but mainly to tick down on opponents. I only put 1 point in Bandage Toss early because you really only us it for picks and stuns. Its not an absolute go to ability right in the middle of a fight, but it is an amazing way to initiate one.
Pros / Cons
With my specific build, the only real issues are the first few levels, some mages, and any champ who builds early crit. Amumu isn't very useful until he has his ult, or he gets lucky and lands on some low health opponent. Mages should always run from Amumu as fast as they can. Maybe a skilled Veigar could land his stun and boom an Amumu down early, but that is very debatable and very unlucky for the Amumu if that happens. Also, early crit champs like Yasuo, or Hou Yi, these COULD be a problem in early game, but that is a very debatable "COULD".
Pros, however... once you get your core build online, absolutely no champion is safe alone, and you can most likely 2v1 or 3v1. It will definitely take some serious fire power, or really bad decision making to take down Amumu once his core build is up.
Creeping / Jungling
Where people start at the beginning of a match is really up to them, but I have a set route to start, that I never stray from. Start at the chickens near mid (Wont need to leash or Smite, and this will level you for Despair), then move to Red Buff right next to it (Health pots should be gone, so Smite this buff for the health. Then go directly to Toad (Smite right away so you're not wasting the poison use) then move to Blue Buff right next to him. Back for the first part of Sunfire Cape and maybe 2 health pots. Then go to Boulders, Chickens should be back up, Wolves, then down the Turtles in river. You should have your ult by this time or really close to it. When invading camps in the enemy jungle, make sure you have health, wards, and at least one charge on your Smite. By this time you should have your Sunfire Cape and Boots online, so feel free to move around as you please. But make sure to be extra aware when in enemy jungle. Try to make good decisions.
Its always best to have great communication during the match. That is the most important rule for every role and every champ. Team should be dropping wards constantly to help play defensive, and to help you be aware of whats going on so you can make the best decisions you can. Because with this build and guide, you can be the carry or the game changer. Remember, as Amumu with this build, you can set the pace of the match. Decision making is where you either make it or fail. Amumu can in fact sneak up behind 5 enemies, Bandage Toss in, Ult, and you'll hurt every single one of them, and stun them. But Amumu is not invincible. So make sure you have some kind of help.
Even if you're a complete fresh fish to League, or Amumu, this guide should help you, and I hope it does. Thank you for your time. Good luck, and have fun!