This is my guide to AP Mordekaiser, it may not be to your liking, but, I find it fun :D. I Chose AP Mordekaiser because with the amount of AP that you should in theory have you'll be able to nuke down your enemies with ease and get those all important kills. And will all everyone stop commenting on this build saying that he's a tank and this should have some tankish items... but it does... but there shouldn't be loads of them considering it's an AP build.

I'm choosing AP runes/5 Runes because they give more AP than the flat AP runes by level 6 and by level 18 they give quite a bit more.

I chose 9/0/21, I did this because with the utility you get the reduction on summoner spells from Presence of the Master, meaning a shorter Ghost cooldown so that you can use it more often to possibly finish off a low hp champion or push faster, maybe even escape death... That's why I put a point in Haste, as you run faster for longer. Also, Intelligence is a great one to have for Mordekaiser. Being able to cast faster means you can recharge your shield quicker + dish out more damage. Quickness... 'nuff said, the extra run speed can also help you with that champion that just managed to escape your grasp, it also pairs nicely with Ghost for that extra bit of run speed. Good Hands is great, it's pretty self explanatory though, the 9 in the offensive tree are due to the fantastic AP increase, Cooldown Reduction and the fantastic 15% Magic Penetration.

Your summoner spells should be an obvious choice... but if it's not clear, I'll explain... Ignite and your Ulti are an amazing combo for that champ that ran away(if ghost is on CD) or if you die and they're on pretty low HP your Ignite and Ulti will finish them off. Ignite is your extra DoT that you will need with your Ult. With these two combined, even if the enemy champion gets away from you, the DoTs can still kill them. Ghost as i said in the Masteries section is for chasing and escaping.

I choose to max Siphon of Destruction first because it will be your main source of damage and with the amount of AP that you should have... it'll be powerful as hell... considering it gains 40% of AP.
I get Creeping Death at level 2 as it's a lot of damage and it's great for minion farming, it gets 15% of your AP which will make it do a lot more damage the further into your build you get.
I get Mace of Spades at level 4 because it gives a bit of damage, but it's not really viable to max it out 'til the end as it scales with AD the best and not that well with AP making it not really as good source of damage as the likes of Siphon of Destruction or Creeping Death, so I choose to leave it.

First I buy Boots of Speed because the extra movement speed is great for chasing those pesky champions that only just manage to survive your wrath. Then I buy Sorc. Shoes as they give 20 Magic Penetration, that could be the difference between life and death for your enemies, If you wanted to go with Health Regen/Survivability route, I would suggest you take Doran's Shield or Regrowth Pendant so that you can do that all important harassing and also you can stay alive for longer, Personally I would take Doran's Shield due to the other stats.

Next I buy Mejai's Soulstealer because every kill/assist you get you will get more and more AP, making you even more OP, and when you hit 20 stacks, you'll get 15% CD reduction, that's just the icing on the cake really, that means you'll get tonnes more Siphon of Destruction's and obviously means... well... tonnes more damage :D.

I get Haunting Guise next as it's quite a nice HP boost, making you survive that little bit more and even more Magic Penetration, enabling you to be able to kill people even faster than before.

The choices of Needlessly Large Rod and Rabadon's Deathcap are just plain obvious... Major AP from the flat stat, the 30% extra AP is just OP, so the more stacks you get, the more AP you get, the more damage you do and that results in more kills, getting you more stacks and the cycle just keeps going.

I get Rylai's Crystal Scepter next because of the pretty big AP boost, along with the 500 HP(More Survivability) and the slow... ah the slow... what a beautiful passive to have on an item... chases and killing are made SO easy because of this slow.

After Rylai's I buy Abyssal Scepter, this item is just amazing, 20 Magic Resistance reduction on nearby enemy champions is fantastic as this will allow you to do even more damage. The AP will also allow you to do even more damage, the magic resistance is just a survivability bonus on your behalf.

Last but not least, I would sell Haunting Guise when I can afford the Needlessly Large Rod and then buy Zhonya's Hourglass, the 100 AP is insane and the use on it is pretty insane for team fights, 1 vs multiple target fight, just poke it and wait for some CDs to come off. Also it's armor... well... that's just a huge survivability bonus.