Spirit of the Ancient Golem - best jungle item for tanks which grants crazy amount of hp late game and is only 2k gold , thanks to this item you will reach around 3.8k with this build.

Mercury's Treads - tenacity , + needed Mr as your only mr sources will be this + banshee's veil.

Sunfire Aegis - amumu does dmg by just "messing around" , his kit is designed in the way which forces him to be close to enemy champions (if he wants to do some dmg), sunfire seems to be perfect to increase that dmg.

Thornmail - great to damage assassins and adcs , allows to duel with them ,with 3.8k hp can harm them significantly

Banshee's Veil - obvious , to get mr , hp , to resist abilities

Liandry's Torment - increase the dmg of W by 1% , from 2,7% to 3,7% , +hp +great passive which triggers on many targets since mumu abilities are aoe

This build grants around 3.8k hp , 260armor , 160mr , which is not bad in the means of being tanky ,plus with Sunfire Aegis , Thornmail, Liandry's Torment can harm enemy team badly.