Why AP Rammus?

AP Rammus is a mobile assassin capable of bursting squishy carries with little counterplay. Once you have homeguards at 20 minutes you can start making plays around the map with your teleport surprising many players with your burst. Each time your teleport is up you create pressure around the map just by the potential to teleport and kill any carry who is farming while extended.

AP Rammus is a fun off-meta build to try out with your friends in normals or while on a smurf, I wouldn't recommend it for ranked since many AP items such as Rylai's Crystal Scepter and Zhonya's Hourglass have clunky build paths that have a large payoff once they are completed but while they are just components leave you very weak.

The surprise factor that I mentioned before is important since most people assume Rammus won't deal much damage.

It's a very OK build.

With the 5% CDR from masteries (45% cap) and the 10% from runes you have a decent amount of CDR, situationally you can build more but if we invest too much money into CDR we won't have enough gold to buy AP to burst a target, which is our primary objective. The runepage is a pretty standard page, I choose to take the 3 scaling magic resist glyphs, you can opt to take 3 more scaling CDR glyphs if you would like.

You can also choose to take Runic Affinity on the 2nd line of the resolve tree instead of Assassin, but I feel that the Assassin mastery helps us kill a target. Having red buff for a bit longer will help our ganks but we're mainly power farming the jungle, the blue buff would help us farm, but that will go to the midlaner, so I chose Assassin.

Another mastery option would be Stormraider's Surge if you are against blue Ezreal, or a midlaner with Frost Queen's Claim and a blink, such as Kassadin, since the burst from Thunderlord's Decree is useless if you can't stay in range of the target champion.

In the jungle I rush Rylai's since it gives survivability and a decent chunk of AP, it also allows me to rush distortion enhancement on Sorcerer's Shoes before I make my first homeguard teleport.

If you're laning it's better to rush Rod of Ages since it will give you sustain in lane but Rylai's will be your 2nd item, once you get your deathcap 3rd you will be at your peak strength. It's probably worth waiting for distortion unless your team is very far ahead since as a laner you have a reliable source of income (minions) which means you don't have to get ahead through kills.

Jungle: Runic Echoes -> Boots -> Rylai's -> Deathcap -> Haunting Guise -> Zhonya's
Lane: RoA - > Boots -> Rylai's -> Deathcap -> Haunting Guise -> Zhonya's

These are standard builds, if you're against a lot of AP it can be better to go Abyssal Scepter, in the event that you are building Rabadon's Deathcap and go base with 1500g don't be afraid to buy another Needlessly Large Rod instead of waiting to finish Deathcap / Zhonya's if you have TP up or you know there will be a teamfight soon.

Taking W first since we have a leash helps us to stay healthy in our first clear which is when we are weakest.

Taking a point in W, Q then E makes our ganks potent as is normal on Rammus.

Q max since it is our main source of damage, E max second so that our target will stay in range of our ultimate once we hit level 6 nothing too strange here.

If you are jungle you farm until you see a potential gank or potential kill in the early game. You could say you're turtle-ing for items.

At 20 minutes try to have already built distortion enchantment and make a homeguard TP play, to do this start charging Q then channel teleport, this way you will be able to engage faster than casting Q after completing your teleport. You Can us this to force favourable teamfights or assassinate immobile champions and then secure 1st dragon if it hasn't been taken, otherwise take towers. 2nd dragon is less important than towers so if you see the enemy team grouping for their 1st dragon I think it is pointless stopping them, instead head top and take a tower with your laner.

Late game is more of the same from midgame while trying to look for opportunities to take baron, also watch out for the other team if they are hoarding dragons trying to get the 5th dragon buff, 5th dragon is stronger than baron.

Positives:

High Burst
Mobile
Global Threat
Split Pushing

Negatives

Item Dependant
Weak Teamfighting until Zhonya's Hourlgass is completed
Not Versatile, if there is a champion too strong for you to push against or you are too weak to kill the ADC or mid you are useless.
You will get flamed
If you lose you're probably getting reported

This build is inferior to standard tank Rammus in almost every way, but it's a lot of fun when it works. This has only worked from me when I've smurfed in silver from diamond so take it with a pinch of salt.