Well, I'm sorry to say but your guide layout isn't really all that good :/ It all feels spammy and you seem to overuse most elements, like colouring, images, and textwalls... I can't really say that I liked it. Build can be said to be fine, works if the situation permits it, but I honestly don't care about build accuracy :/ I believe you should try to update your looks, because I can't say you deserve third place with this. For now, I'm going to downvote, but in case you update it and make it look better, PM me to come back and give you my opinion again.

this build is very situational, and I think will rarely be the best build for the situation. getting shurelyas, randuins , fh and aegis is much more important than rylais and haunting guise.

spirits visage is a more early game power item, and you are wasting a slot for it late game, especially when amumu can't heal. I don't know why you don't want shurelyas, it's the game changing item.

also, amumu is an extremely strong ganker when done properly, and his easiest lane to gank is actually bot, because your lane can cc for you , and the enemy will die very fast.

boots of mobility is basically bought on every jungler at the moment.

u don't mention lane ganks, or making calls as the jungler. dragon and baron is ur responsibility.

so much to reply too >.<

Rylai's Crystal Scepter has both HP and AP which Amumu can use and the slow is a bonus that Amumu can also use with his abilities especially on Despair. It isn't a core item but it isn't bad either and it will boost your damage output and overall tankyness.

AP on Amumu isn't as effect as before the nerf but damage is damage and I mostly built Spirit of the Spectral Wraith not because of the AP but the CDR, mana regen (since i give 2nd blue away most of the time and that I use Bandage Toss frequently), and the Spell Vamp (i like to start my ganks with full HP)
Same goes for Hextech Revolver, a decent amount of Spell Vamp can heal you up after you take some damage from a gank). I could go for health regen but it wont help in a teamfight and spell vamp heals more as you gain more AP (too bad it doesn'y apply to Sunfire Aegis's Magic Damage)

Mobility Boots is great for early game and gets you where you want to be late game but its more on preference since it only helps u get around and a good chase. I depends on whether you prefer utility over defense. But I do have to agree with the the boost this item gives to Amumu's Map Presence as he will appear more often.

A few people actually told me to use Movement Quints instead (As well as other substitutes like Gold per 10, Spell Vamp, Flat HP, etc) If I did use Movement speed quints then I'd buy Mobility Boots since the quints will boost the passive movement speed. This I will have to test out once I get myself some IP (I have other runes to buy before Testing)

Even though you Down Voted, I'd like to thank you on putting a lot of thought in your comment with detail, it's gonna be something I will relook at when I decide to make some changes.

A down vote from me, I'm sorry to say.

Your AP build doesn't make any sense to me. It's an interesting idea to do something different but Hextech Revolver gives you flat AP which got worse on Amumu since his scalings got nerfed, so magic pen is better because of his good base stats.
I would always get Mobility Boots on your first back. You can quite easily save up the 1000 gold before backing (especially with a successful gank) and you will have so much more map presence afterwards since the enemy can now ward early and you won't have an Oracle's Elixir to counter it. Your clearing will be quicker, your ganking will be better and it won't hurt you to much. Then I wouldn't upgrade the Spirit Stone early on. It gives you ok sustain for the early game.
Rylai's Crystal Scepter hell I see this on every Amumu guide by now and I just don't agree. The 15% slow is just a minor thing and the time it takes you to actually get this (overpriced) item just for a tiny slow, health and flat AP (not that good as mentioned before) is to long. If you get your Rylai's as the third or fourth item then you will have enough ranks in Bandage Toss to stick just fine. Also if you have Mobility Boots you'll get to think differently about speed ;)
Only thing I agree on on the AP part is the Haunting Guise. I get it if I get ahead and feel like getting more damage. But that's more cheese than anything else.

Two more things:
- I would recommend starting with Tantrum since it gives you more damage and damage reduction from the wolves and blue buff.
- Get some Movement Speed Quints. It adds up so well with the Mobility Boots and you won't ever miss your Rylai's!

I wish you all the best with your guide and I'm hoping for a reply
Cortez Cardinal

Don't buy a Sightstone early, get Sight Wards or Vision Wards instead. Later it is a good option, but not on first back.

Nice guide, made me play and love jungle mumu again. <3

+1

Awesome guide, but i prefer taking Bandage Toss at lvl 3 for early ganking and usually, i max it second to lower the cooldown, because it's awesome ganking tool. But yea, very nice guide! Left an upvote :)
EDIT: I also think, it's better to investigate mastery points to Tenacious - not to that tiny bit of magic resist from Legendary Armor and Resistance . You also don't really need that Reinforced Armor , so you can have 15% Tenacity from masteries and 35% or so from Mercury's Treads or that ancient golem thingy, wich is already 50%!

Don't forget you would also be able to gank earlier
BTW you forgot a wolves camp on the guide, before red buff

I tried the jungle route you suggested
I ended up with More Health and it does save time but i ended up with less gold, around 600g when the other route I ended up in about 700g
Considering the passive gold gain and other clears after your route is more effective and the end results were better too
Voters now have to make a comment
Thanks for your thoughts and suggestions
Might work more on it over break

Make comment to vote to not get troll voted.
wolves->blue->wraiths->wolves->red->wraiths->gank lets you get to level 4 earlier.
Starting with sightstone will put you behind so much, you should get it a little bit later in the game in my opinion.
color the guide a bit and make it more fun to read.
overall a nice guide, but there is a lot to add and explain.

Solid S3 guide, with an item path that makes an amazing amount of sense.

IMO, Tenacious and Legendary Armor are both viable choices.
Tenacious is a good pick for that early game CC Reduction since it takes a while to build Spirit of the Ancient Golem. But Legendary Armor is also a good pick since a 2% increase late game can add 4 Armor and 2 Magic Resist about for only 1 Mastery Point while Tenacious takes 3 for 15% CC Reduction.
Like most choices, it depends on who you're fighting and a player's play style.