First Amumu guide, apologies if I suck. First off, I love playing Amumu. Let us go more into the guide and my experience with Amumu as we go on through my guide.

Quints: Movement speed quints because when pre gank before lvl 6 ur gonna want to auto attack the enemy. Why? well you passive. It reduces the enemies magic resistance and while your despair is on it does a decent amount of damage. You will need to catch up to the enemy which is usually running away and poke at him. (Remember to auto-attack)

Marks: Magic penetration, is considered to be better than flat AP/AD. I honestly like flat AD on AD champs and such, but magic/armor penetration is considered to give an advantage and is most likely for you to be aggressive in lane. In this case your juggling I hope, you gank a lane and magic penetration would help you get kills or give kills to your ally. Magic penetration on Amumu is great because your despair is just to good. (Remember to auto-attack)

Seals: Armor op.....HANDS DOWN (Remember to auto-attack)

Glyphs: Magic resist......HANDS DOWN (Remember to auto-attack)

9/21/0
OFFENSE
Junglers are usually supposed to engage in battle and try to get someone off guard or group the enemy together for wombo combos or obliteration. So there's Amumu who goes into battle and gets the enemy team to group up and die. Expose weakness is good on Amumu because every spell he does is just op. Every bit counts so 1% increase to allies damage is pretty good. Don't forget your magic penetration and despair. (Remember to auto-attack)

DEFENSE
Tough skin and bladed armor is for jungle sustain. Now for tenacious, it is to help you survive your dive on the enemy team. The rest is pretty standard. (Remember to auto-attack)

Now you will just have to grab Hunter's Machete because why wouldn't you? It is to help you sustain in the jungle. Now even though Sunfire cape is your core item you got to make hunter;s machete worth something so buy Spirit of the Ancient Golem. Then no matter what go for Sunfire cape after you complete Ancient Golem. The reason fire cape is the core item is the magic damage. You guessed it, Sunfire cape works well with your passive cursed touch. Your Firecape along with your despair will burn and give a heart feeling touch to you opponent. Your magic reduction will be to great for the enemy to catch up in magic resistance so auto-attack your enemy to death. (Remember to auto-attack)

Despair is not a bad start to jungle with, but tantrum is reduce damage from physical attacks and gives you a .5 sec cooldown on it. EVERY BIT COUNTS. You wouldn't wanna kill them lizards while taking Golem with leash. It might not give you lvl 2. There's no reason you shouldn't smite so SMITE! (Remember to auto-attack)

Now maxing out despair is no trouble at all but getting physical attack damage reduction and cooldown is awesome. So tantrum is pretty smart move to max out. (Remember to auto-attack)

Now Amumu is viable in lane but not the strongest in lane so taking any other summoner spells besides smite and flash is going to be a gamble. (Remember to auto-attack)

Clairvoyance.....sigh* what are you doing.... (Remember to auto-attack)

Ignite: okay spell but a gamble. (Remember to auto-attack)

Teleport: okay spell but a gamble; good for you to get back in lane when recalled to get more sustain items against your counter part. (Remember to auto-attack)

Clarity: good spell not the best, a gamble. (Remember to auto-attack)

Barrier: good spell not the best, a gamble. (Remember to auto-attack)

Cleanse: good spell not the best, a gamble. (Remember to auto-attack)

Exhaust: good spell not the best, a gamble. (Remember to auto-attack)

Ghost: good spell not the best, a gamble. (Remember to auto-attack)

Revive:...........(Remember to auto-attack)

Heal: good spell actually. (Remember to auto-attack)

Pros
~Strong ganker pretty efficient ganks
~Awesome ult; strong, massive AoE damage
~Fast jungle clear
~Large amount of CC
~Tanky while retaining a high damage output
~Easy to learn
(Remember to auto-attack)

Cons
~Squishy but will overcome
~High ult cooldown but will overcome
~His story is sad wish he can one day see his parents
~Crybaby
(Remember to auto-attack)

Anyone with a simple AoE is good synergy with Amumu (Remember to auto-attack)
~Katarina ult plus Amumu ult= OP (Remember to auto-attack)
~Morgana ult plus amumu ult= CC all day (Remember to auto-attack)
~Kenne ult plus Amumu ult= CC all day (Remember to auto-attack)
~Zyra ult plus Amumu ult= CCall day (Remember to auto-attack)
~Fiddlesticks ult plus Amumu ult= OP (Remember to auto-attack)
~Galio ult plus Amumu ult= OP (Remember to auto-attack)
~Gangplank ult plus Amumu ult= Decent damage; Gangplank's ult is based on chance (Remember to auto-attack)
~Hecarim ult plus Amumu ult= can probably wreck adc in a sec (Remember to auto-attack)
~Jarvan ult plus Amumu ult= CLEAN UP for adc or mid laner (Remember to auto-attack)
~Karthus defile plus Amumu ult= OP if Karthus does a decent amount of lay waste then ults (Remember to auto-attack)
~Leona ult plus Amumu ult= Clean up for adc (Remember to auto-attack)
etc