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This build uses Bami's Cinder items and Rylai's Crystal Scepter as its core.

~Flaming Graviton~ provides TANKINESS, CROWD CONTROL, GOOD DPS, MAP VISION (via Tracker's Knife).

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The ~core~ items for this build are:

* Bami's Cinder upgraded into Tracker's Knife - Cinderhulk grants consistent local magic damage output, with increases in DPS with every level Amumu gains.
* It also boosts Amumu's HP by 400 which helps make him tankier.
* It will do substantial damage which complements Despair. It will not activate Rylai's Crystal Scepter's passive slow.

* Rylai's Crystal Scepter provides local crowd-control via it's unique passive slow.
* This will raise the effectivity of his ganks. Since the slow activates on enemies through Amumu's skills, this synergizes extremely well with his Despair skill.
* It also boosts Amumu's HP by 400 which helps make him tankier.
* Granting 100 AP, it once again synergizes with Despair, as every 100 AP increases Despair's damage.
* IMPORTANT: If the enemy team is High AD, put this off and build some armor first.

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Having finished these two core items, any further items should be acquired with the objective of withstanding the enemy assaults as a tank.
The standard three types of enemy champions will be High AD, High AP, High HP or some kind of mixture of the three.
See the build guide above to get an idea of what might help you stay alive for as long as possible.

Game-start, jungle-clearing route.

Starting with Despair.
1) Gromp: (Heavy leash required). Smite used. Tantrum picked up.
2) Wolves
3) Chickens: Bandage Toss picked up.
4) Golems: Smite used.

Back.

1) Red: Smite used.
Red river crab (optional).

2)Gank mid, but don't stay long. Amumu is still too squishy.

3) Blue: Smite used.
Blue river crab (optional).

Back.

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Ganks:
Early level ganks should be quick and accurate. Amumu does not start out as a tank and the first items acquired do not grant HP. Do not attempt to use him as a tank until you have finished Bami's Cinder at least.

The best jungling ability that any jungler could want is a gap-closer, which Amumu has in Bandage Toss. Use it to initiate your gank.

When initiating a gank, activating Despair before you use Bandage Toss will save you time and effort, just remember that Despair will quickly run you dry of mana.

This sequence can also be carried out in reverse -- walking in to the gank and using Bandage Toss to catch and stun any escapees.