this is my jugnle amumu build, most of my build is absed of of other top builds here on mobafire, start at blue golem need a leash just to makes things easier although you do not need to have it, as for the runes i use it depends on what kind of mood i am in, if i feel like realy dealing somdamage i will go with more of a ap rune page just so that my e has a little more burst, but amumu is one of the best tanks in tha game so a fairly standard tank page works perfectly fine with him. magic pen red, dodge yellow, mr blue, and health purple. i go with ms purple now mainly because it make you that much faster and allows you to land more bandage tosses which prevents many of those veiagrs that get away with 30 hp situations from happening. my ganking inittion sequnce is flash(if neded, somtimes they are jsut in range of bandage toss anyway, q, then ult, or q to a minion then flash then ult, have ur w on and hit e imidiatley after landing ur ult so that u get that damage off to as many ppl as possible befire they have a chance to flash or dash blink away.rememebr amumu wants to take hits inorder to reduce the cd on ur e and being able to spam e while ur w is on along with sufire ur dealing some nice dps, when jungling i will usually take the first 2 blues before giving it up to our ap carry, only excpetion is if i have had a bunch of succesfull ganks and was able to get a catalyst early or of our ap carry is 7-0( u get the idea) and i have no problem giving it to them because they are clearly dominating, and i would like them to keep that advantage as long as possible. as for red buff i will sometimes jsut let our ad carry get it early because amumu does not really utilize it all that well, and since u are the tank, u need to let ur carries do their job.but after the first one it will always default to ad carry.
as for getting bv, which i do not know how some amumu do not get this, i will always get this just to insure that i land my ult, i dont know how many times i have had an amumu on my time fail to get ult off because they got stunned or snared and allowed the other team to get away, getting maybe 2 ppl in the ult, instead of 3+, now unless for some reason u are in a game where there is 0 cc on the other team(like 0.001% of the time) no bv is acceptable, but amumus ult is the most important part of amumu stunning the other team for that long guaranteeing that one of them will die instantly and 2 more will be at half health or less, while your team is still relatively high in health still.