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.
Guide to Tank and Spank Amumu.
I like this build because it gives me good damage while also making me rather hard to kill. Their are several ways of going about this build (depending on the opposing team).
An Easy Farm
Start out with Regrowth Pendantand a Health Potion.
Farm until you have 350 gold.
Then Port back and buy Philosopher's Stone.
Use your Teleport to get back in the action asap.
Farm farm farm until you have enough to buy Boots of Speedand Giant"s Belt. (note: you may die some at first so buy boots and belt whenever possible.)
By now you should have a good number of kills, or assists ( if not, go jungle for a bit till you can get your next item.)
Buy Mercury's Bootsand the Most important Item for amumu Sunfire Cape. (this is where you really start tanking and spanking.)
Now the next item you get really depends on your team and how you are doing as a team. If you are doing real well and not dieing very much so with Abyssal Scepter. If you feel like you are dieing a lot and you cant tank for your team get Guardian AngelFirst. Either way you will get both items, when just depends on how comfortable you feel when you have the gold.
The last main item really depends on the opposing teams carry. If its an AD ( attack damage) chamption id go with Thornmail. If the carry is ap (ability power) id use Force of Nature. If they dont have a carry but keep CCing you (crowd controlling) go with Banshee's Veil.
Now if you have gotten this far in a battle and have an overflow of gold sell your Philosopher's Stoneand buy either one of the items mentioned before ( depending on your opposing team) or buy Zhonya's HourglassZhonya's hourglass will give you a boost to your magic damage and also save you if you get low on health.