This build is based on my wast experience playing Amumu as my main champ. I have tryed lot different builds but whatever they change amumu stays great tank/assister with great damage output(in longer games allways 300k+ dmg which is 85% magic damage, so in combination with his passive....)

All runes should be armor and magic resistance. My very succesfull alternative was AP Quintessences and other armor and mr (all seals and marks go armor and all glyphs go mr).

Basicly it works same except if you skill bandage first, then AP could be better...

As for masteries you could take exhaust mastery or one for ignite if you are taking the ignite...

Everything else is on you except you should get yourself utility mastery which gets you more exp... it is significant advantage for you since you already are farmer.

And yeah...ummm... do not EVER get dodge items on amumu... read E skill description for "why".

here are alternatives:

Exhaust/Teleport - you have additional immobilizing(kinda) skill and teleport for better covering the map.

Exhaust / ignte because people tend to start running away when it is too late to save yaself from good timed ignite.

Heal / claryti - Amumu is tank and highly dependant on mana

What i did not include are potions... you need lots of mana, so from time to time you might use a mana potion or two. Also I wanna suggest to buy regrowth pendant earlier in the game if you are having hp issues and use it later for warmog's.

Other items I recommend:

-Force of nature(preceded by Negation cloak earlier in the game) if there is high AP dps caster (ryze annie veigar etc) in opposing team. You get negation cloak right after sunfire cape and fore of nature after warmogs(op regen rate).

-Thornmail also right after sunfire cape if you have yi or similar abusingly high physical dps in opposite team and he is getting pumped up(if he is not getting fed just forget about this and processd with build).

-If game gets on and you finish this highly expensive build just go on with another warmogs or smt like that(it is not unlike to happend.

Aumum is best farmer there is. That's it. You just go around and get gold... After you get enough mana, you still need to get mana buff whenever you can, but you are goldfinger of LOL.

Whenever you go through jungle, you can clean it on the way really fast and you have very high aoe magic damage output so you kick *** at minion farming(filling warmogs almost too fast.

I love laning with casters - Amumu's passive gives extra edge to every spell you cast. What I am talking about is - whenever you start fight caster should cast right after unit is being hit by Amumu. For this I prefer Fiddle.

Everything else about team work(For any tank, but especially amumu):

-Stay in fight as long as you can.
-Use your stuns for initiation(bandage toss) and cc when you are winning and they might want tot run or everyone else needs to run away.
-Die for others to kill.
-Never stay without mana.

Pros:

-You create victories
-You control teamfights
-You can solo nashor
-You earn lots of gold
-You rock
-You can rambo after lvl 12 in 80% of cases.

Cons:

-You will get 29 assists and do 300000damage so if you love killing ppl, just miss this one.