AMUMU BUILD AS TANK
The most common way to play Amumu is a hybrid between ability power and tank stats. This lends Amumu well to items that have cooldown reduction, ability power, health and defensive stats. Naturally, this makes items such as Cinderhulk, Liandry’s Torment, Abyssal Mask, Frozen Heart and Rylai’s Crystal Scepter. However, if the other team has a critical strike based marksman such as Jhin – or even a mid lane Yasuo, then you should consider Randuin’s Omen.
One of Amumu’s strongest basic abilities is Despair ‘W‘, which requires a lot of mana. Likewise, Bandage Toss is also gated behind mana and so your ganks need to be successful unless you have a blue buff. This is one of the reasons why Frozen Heart is a core item on Amumu. Not only does it give you access to an additional 400 mana, but it also opens up 20% Cooldown Reduction into your build. This also benefits Curse of the Sad Mummy and Tantrum, since both abilities are gated behind cooldowns rather than mana.
You should avoid building tank items such as Warmog’s Armor and Dead Man’s plate as they don’t offer many stats outside of health and armour. Instead, you should choose Cinderhulk for your core health item and Frozen heart for armour.