For those of you who play Amumu, this guide will hopefully give you another way to play one of the most powerful heroes in the League. For those who have not yet tried the sad mummy, or are just starting to learn him, this is a very straightforward tank build with high upside as you improve your level of play.
Very simple runes for this build, I haven't found any other runes to work better;
Health Quints - You're a tank first and foremost
Magic Pen Marks - Your damage will almost all be magic based, but people won't counter your damage, so a little magic pen should put most heroes at 0 MR
Flat Armor Seals - Good for anything Amumu wants, from jungling to soloing
MR/Lvl Glyphs - Helps scale against casters, the only heroes that can burst you
Some people like evasion runes on tanks, but I feel that they minimize Tantrum too much, which is undervalued in team fights when people see Despair and Curse of the Sad Mummy. Other people want movespeed quints, but I find that the bonus health is too important in the early game to sacrifice. The only other rune that should even be considered on Amumu is cooldown reduction, but this is a tank build, and your most important skills will have 0 (Despair) or very little (Tantrum) cooldown.
I use a slightly off 0/23/7 Mastery page, simply because I like the 2 extra points in Initiator over the last point in Swiftness. The general focus of the masteries is simple:
Take Less Damage. Seriously.
Tantrum already reduces incoming physical damage by 10, Honor Guard reduces all damage by 1.5%, Indomitable reduces all damage by 2, and Tough Skin reduces minion damage by another 2. Add this to the bonus health from Durablility, Veterans Scars and your runes, then add the armor and magic resist from masteries and runes, and you have a tank that can almost afford to take hits for nothing.
Oh and Juggernaut. It's a little bit unfair in my opinion, so take it.
This is where the build gets creative. The finished items listed are my most common ending items, but I almost never have all 6 together. The key items in this build are the early items. Philosopher's Stone is a great item, giving you extra gold to feed the decently expensive build, plus HP and MP regen, great for a tank. Heart of Gold is a slightly worse, but still great item on Amumu, again for the Gp5 and health on a tank, with the added bonus of being a piece of Randuin's Omen.
I try to get the Philosopher's Stone and Heart of Gold in my first trip back, with basic boots if I am doing well.
Once you have the two gold per 5 items, the game becomes a little faster. You can worry less about last hitting, and more about keeping your opponent from farming, since you will most likely be making 1-2 more gold per second than your opponent. If you can farm a bit while harassing, all the better, as this build snowballs into bigger and better items.
Once i need to go back, I try to get the Giant's Belt and at least a Regrowth Pendant, while finishing Mercury's Treads, hopefully you'll be even closer to Warmog's than that.
Now the game should be picking up, with teamfights starting to show up and towers beginning to go down, and because you're playing Amumu, you need to be a part of evey single one. Try not to take kills, and don't be afraid of dying, because being 0-6-15 is not uncommon and not a bad thing. That's 15 kills that your carries hopefully got, and killing you is now worth less than 150 gold.
During quiet times, finish Warmog's and start filling it, then focus on the Force of Nature with your farm gold.
Now that you have a couple big items, chances are most of the enemy team does too. Pay attention to their team comp, and individual carries that are doing well, and build accordingly. If you see Tryndamere or Master Yi, don't be afraid to finish a Thornmail early. If Veigar is bursting you down, try Banshee's Veil or get the Negatron Cloak for FoN.
Items after your gold per 5 and Warmog's are up to you, and it all depends on the game, but remember, YOU'RE a TANK, so don't be trying to play AP carry Amumu. Support your team and counter their heroes so that your carries can do their job.
Other items that work:
Abyssal Scepter - MR, AP, and a passive that works well with Amumu's passive
Rylai's Crystal Scepter - Health, some AP, and a passive that combos with Despair
Rod of Ages - Health, Mana, and AP in large quantities
Sunfire Cape - Armor and HP, with a passive that ups your low damage
Manamune - Mana to feed Despair, with some autoattack damage for pushing
Guardian Angel - It works, but you shouldn't care so much about dying
Ionian Boots of Lucidity - CDR, if you want to deal more damage and they lack CC
Trinity Force - It's the most expensive item for a reason, if you have 4k to blow, try it
A very common skill sequence for laning Amumu, one level in Bandage Toss for emergency stuns and ganks, then max in order:
Curse of the Sad Mummy
This is a solo lane Amumu build, so try to use Despair lightly, last hit with Tantrum and harass with Tantrum. Save your ult for teamfights, and don't be afraid to turn around and Bandage Toss the hero chasing you, that extra second of regen can buy you just enough time for allies to get there, or enough tower shots to Tantrum and ult for a kill.
Basically, win with Tantrum, but remember what character you're playing and that you have 2 stuns to turn fights around with.
With the rebalanced/remade summoner spells, I find that solo Amumu is a viable way to play premade 5 v 5's.
Promote gives Amumu a way to last hit without being harassed, a way to push towers without eating too many hits, extra damage against an enemy hero, and a minion that can defend your tower while you deal with a gank or another hero. This is the key spell for a solo top Amumu.
Flash just barely edges out Teleport for the second spot, solely for the synergy with Curse of the Sad Mummy. Flashing past their tank to trap the carries in your ult, then chasing with Bandage Toss can disrupt a teamfight like no other hero can.
Teleport - Gets you back to your tower without missing waves, lets you port into other lanes, but does not help when actually fighting, so the edge goes to flash
Cleanse - A great way to escape ganks and keep mobile, but with 45% Tenacity, you really shouldn't need it
Pros / Cons
High Health and Health Regen
Gets expensive items quickly
Great chasing speed
Good gank escapes
You're playing Amumu
Low physical damage/burst
Low mana base
Low turret pushing ability
Dependant on allies for kills
Hopefully this guide has given you some new ideas about how to play a character that is typeset into a "jungle hard, win dragon"/"bot lane, win dragon" kind of hero.
Remember, Tantrum is your best friend in lane, items are situational, and you're a tank, not a carry. Also, you're still playing Amumu, taking dragon and ganking lanes is not a bad thing, as long as you don't forget to keep top lane clear.
This is my first attempt at a guide, comments are welcome, criticism is appreciated if polite, and remember to have fun playing LoL, it is a game still.