Hello friends,
This is my first build guide but before you dislike please try my build and strategy. Before we begin I must let you know that this build does not work for everyone and was made while screwing around in a custom game and has been tested many times in ranked matches. This guide explains the thought process behind my choices and what I reccomend you do throughout the game.
I use this build playing a support/tank bottom lane accompanied by an AD Carry. Amumu is very good when put with a Miss Fortune, Ashe or Ezreal. This build is designed to devastate enemies while being extremely durable and it also allows Amumu to reduce enemy defences by terrifying amounts.

WARNING: This build may not work for all players.

Pros

Amumu has a lot of CC
Amumu has lots of damage which can result in being focused (keep in mind this is a tank build)
Has a game changing ultimate
Has a lot of AOE and per-second damage
Very tanky

Cons

Can be mana hungry early game
High cooldown ultimate
Slow skillshot stun

You may be questioning my choice of runes for Amumu. I have chosen to invest in a lot of health because Amumu can be squishy in the beginning of the game. Health runes ensure that Amumu can take signifigant damage early game allwoing him to be very effective during the laning phase. I have chosen Mana regeneration per level because as the game goes on Amumu becomes more and more mana hungry as his cooldowns are reduced and Despair becomes more needed. Finally what would have left you confused is my Attack Speed marks. I have chosen them entirely because my build is designed to bring forward the use of Amumu's basic attack. Buying the Frozen Mallet is a personal decision because it ensures that you use your basic attack as much as possible to keep slows consistantly on the enemy, attack speed simply allows you to slow more often and more effectively.

Regrowth Pendant

The Regrowth Pendant is a very good starting item for Amumu because it gives him long term sustainability so long as you use your mana wisely.

Philosopher's Stone

The Philosopher's Stone is incredibly important in ranked play and though it is not as important in normal gameplay it can still give signifigant benefits to your late game. In ranked play a support or tank is supposed to allow the AD carry they are laning with to get as much CS as they can but when playing with a Philosopher's Stone you become less reliant on killing creeps for gold. The extra health and mana regeneration is also very useful for your early/mid game. Keeping your Philosopher's Stone until the end of the game allows you to accumulate as much gold from it as you can. I reccomend selling it last for an Abyssal Scepter.

Boots of Swiftness

For a tank, boots of Swiftness may not be the best choice, but then Amumu is different. My build is designed to ensure that important enemy champions have very few ways to escape. When Amumu has a high movement speed he is able to keep his enemies within the area of effect of Despair making Amumu very high damaging despite having little or no AP.

Sunfire Cape

Ah the Sunfire Cape. The core item in this build is the sunfire cape because it deals damage in an area of effect, like the ability despair it deals damage constantly around Amumu and taking a Sunfire Cape allows Amumu to deal massive damage per second to enemies nearby.

Frozen Mallet

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The point of my build is to get as much use out of Amumu's passive as possible, reducing Magic Resist by signifigant amounds allowing all of Amumu's abilities to deal much mroe damage than they normally would. The Frozen Mallet slows enemies when you basic attack them and so taking a Frozen Mallet almost forces you to use your basic attack in order to do lots of damage. Frozen Mallet gives a fair bit of health which is very useful because this build includes a Force of Nature, meaning the more health you get, the more health regeneration you get.

Force of Nature

The Force of Nature gives the most Magic Resist in the game along with tonnes of health regen and a little Movement Speed. As you can tell I love getting movement speed as Amumu, combined with the Frozen Mallet but the point of purchasing this item is to get lots of Magic Resist. Often the mid laner deals massive damage to anyone near them and so reducing this damage as much as possible is very important.

Guardian Angel

Guardian Angel is one of my favourite items. When taking it as a tank who rarely dies as it it having the ability to revive is pretty scary for your opponents. Guardian Angel also provides a fair bit of Armor and a decent amound of Magic Resist.

Abyssal Scepter

The Abyssal Scepter is one of the most devastating items you can get for Amumu. It makes him tankier but at the same time it gives him Ability Power. When Amumu is played with Ability Power his abilities are absolutely devastating. The point of getting this item though is because it reduces the enemies Magic Resist in an area around you, combined with Amumu's passive, you can drop the enemies Magic Resist below 0 allowing you to deal 100% Magic Damage which is absolutely terrifying.

I put a point into Summoner's Wrath to reduce Armor and Magic Resist even further than it already is with this build.
My points in Defence are pretty straight forward, prioritising damage reducion, armor, magic resist and health.
Points in Utility are to help with your Flash summoner spell, to give you more max mana and to further increase your movement speed.

Exhaust

Exhaust it quite frankly an OP summoner spell. I always take it to ensure that there is no escape for my enemies and also to stop the enemy AD champions from doing very much damage. Exhaust can be swapped for a spell like Heal if needed and even Ghost if you are a speed demon. I would reccomend taking Exhaust under most circumstances.

Flash

I usually take Flash because it gives you an alternative gap-closer and it is a very effective escape tool. Flash can again be swapped for Heal if needed or again Ghost of you prefer a long term speed increase to a short range blink.

Amumu has a powerful early game but you need to be careful about your mana, try to avoid fighting unless you have enough mana to sustain Despair in a fight.
Amumu, again has a very powerful mid game. Curse of the Sad Mummy allows your team to easily win early teamfights and push further down the lanes.
Amumu's late game is absolutely devastating but you need to prioritise keeping the enemy from dealing much damage. I reccomend attacking the AP caster or the AD carry and ensuring that they cannot escape the fight. Amumu can get fed very easily resulting in the enemy team focusing him which is no problem because your team mates are there to do the damage. Swapping some items late game is not such a bad thing depending on who is on the enemy team and who is succeeding but I reccomend keeping your Sunfire Cape and Frozen Mallet at all times.

Thanks for reading my guide. Like if you liked and dislike if you disliked and please comment with advice on making guides and requests for future guides.
VoidPrison (Apollo 16)