The hew hat is not in Mobafire by now, so you still see a Zhonya's here.
IF YOU DOWNRATE THIS GUIDE PLEASE LEAVE A COMMENT AND TELL ME WHY.

This guide shows you 3 ways to play Karthus. The first one is pure AP, the 2nd one is just MPen, the 3rd, and in my opinion the best one, is a mix of both. The skill sequence and the runes and the masteries are for all 3 the same.
Edit: Haha, now is AP Karthus even more funny, new items xD

Masteries: This are just the normal masteries for Karthus. CD reduction, mana and MPen.
Runes: MPen is allways good with mages.

AP Karthus:

Pros:
- Never run out of mana
- max AP
- great damage

Cons:
- no movement speed
- no survivability

Maths:
This is the way to max out the AP because of Archangel's Staff. One Archangel's will give you 1400 mana because of it's passive and the others will give you 400 each. You get nice mana reg, 45 AP from each Archangel's and 3% from your max mana as AP FROM EACH ARCHANGEL'S!!! That are 15%.
Now let's calculate your max mana:
[1368 (at lv 18) + 1400 + 4*500 (from the Archangels)]*1,05 (5% mana from masteries) = 5006 Mana.
Now the maths for the AP:
[45*5 (from Archangel's) + 155 (New Hat :D) + 5006*0,15 (bonus from Archangel's)] * 1,30 (Hat's passive) = 1470 AP
And now the calculations for the damage of the spells ;D:
Lay Waste: 120 + 1470*30% = 561 (if you hit only 1 target 1062)
Wall of Pain: /
Defile: 110 + 1470*25% = 477 DPS
Requiem: 550 + 1470*70% = 1579

Playstyle:
You should go mid. Always spam your mines, either to kill minions or to harass. Last hitting minions is very important. When you are Lvl 6 you should watch at the other lanes to use your ult in the right moment. In lategame, you should never go into a team battle. You will die because you dan't have any live, tank or movement items. Care for CCers, if you're stunned, you are death if you don't have Cleanse. Same with Silence. In a team fight, stay back and spam Lay Wastes and Wall of Pain, put on Defile if someone comes near enough. in 1v1 you should beat nearly everyone, because with Lay Waste & Defile you do 1000-2000 dmg every second, but you shouldn't run out alone. Remember the big damage of you ult and use it often. If you're dead, activate Defile and spam Lay Wastes and use Requiem after 5 secs being death. That's all.

Now the MPen Karthus:

Pros:
- You will penetrate all of non-tanks MRes
- Also tanks will take a lot of damage

Cons:
- Not much AP --> Don't make that fast damage --> Fighters and Nukes will kill you
- Low survivability
In this guide you will penetrate 120 of the defenders MRes. That should be all from non-tanks and the most from normal tanks. But you don't have much AP (587).

Playstyle:
It's pretty much the same as with AP Karthus, but you can go out alone in lategame because you have some movement speed. Go mid and last hit. With TP you can get back to your line very fast after recall. In team fights you should stay that much back, that you hurt them with Defile, but not any closer. If you are out of mana, it's situation dependen what spells you cast. Is there a single target? Lay Waste. Are there multiple heros? In a team fight Wall of Pain and Defile. Sometimes you should use Requiem, but that doesn't happen that often with this build. You also can last hit some minions to restore mana with the passive from Defile. You see, in this build you have to think more when to use wich casts.

Mix of both:

Pros:
- Much AP
- Much MPen
- Can push towers because of Lich Bane

Cons:
- Low survivability

Playstile
In this build you have 80 MPen, 985 AP 6868 Mana. You will have a nice damage output to all characters. You also can push towers with Lich Bane (every 3 seconds nearly +1000 normal damage). Also with this build you should go mid. You also should lasthit minions and you also should never stay in the front. You won't run out of mana that fast so you can spam your casts nearly whenever you want. If you need a higher survivability, you can skip 1 Archangel's and buy Rod of Ages/ Rylai's Crystal Scepter, but you won't have that much AP. It's situation dependent.


Please leave a comment if you vote and tell my why you think it's good/bad or what i can do better.