Welcome to my Karthus build. In this build I will show you how to build an amazing DPS Karthus that can take some damage.
The main idea behind this build is gaining as much mana as possible. Through this build you can have over 5000 mana, with Karthus. This converts over to ap, which allows for over 1000 ap. If the build above says that you only get like 400 ap, DON'T BELIEVE IT. It doesn't put into consideration that extra ap and mana from archangel staff, or the % from Deathcap

Pros



+High damage output
+Never runs out of mana
+Can guarantee kills after death
+Can go 1v1 against enemy ad carry


Cons



- REALLY difficult to master.
- Have to be extremely aggressive in mid lane with lay waste
- Low movement speed

Some people will be wondering "If your an AP carry, why are your masteries in Utility." Thats an easy question. In the mid, its a race to get to level 6 for your ult. Because Karthus's ult hits everyone at once, it is a must to get it early. By the time you are level 6, the champs on bot are still 3. Plus through these masteries you have 10% cool down reduction. The faster your ult comes back, the more kills you can get.

Flash:
One of the best Summoner spells. This is a must have for Karthus. It allows for an escape or fight.

Ignite:
This is also a good choice for Karthus. It adds to the constant burst. Just a good choice for most ap carries

Teleport:
I don't prefer to use this, but if you need to use it, use it. Its spells like this that could save or destroy a turret.

Just follow the build above, nothing more, nothing less.

Lay Waste:
This skill allows for close combat with ad carries. Lay waste deals 400 damage to the target, and if there is only one target, it deals 800. Plus the 1 second cool down allows for kills in 3-4 seconds. Its mana cost is really low, 20-44 mana. You can use Lay Waste for minion kills.

Wall of Pain:
allows for escape, or kills. What most people don't realize is that it decreases enemy's armor/magic resistance.

Defile:
This is, when untoggled gives you mana for every minion you kill. You are never mana hungry, and if you are, just kill some minions. When toggled, its your "Bread and butter." It deals 300 damage per second, when activated. This skill is nice because if you want to push a lane, all you have to do is walk down it and all of the minions die.

Requiem:
This skill is used to guarantee the kill, never use it if you are not sure, or if you die. If you do than you have to wait until cool down is refreshed. it deals over 1000 damage

Here is the trick to it. Be the mid. Need a jungler, pick another champion. Don't solo top. JUST GO MID. Its not that hard.
In fight of 1v1 activate your defile, than constantly spam Lay waste on your enemy, if you die keep hitting them with lay waste. If they get away with low health use your ult. In team fights jump in the middle of them. Even if you die you help your team succeed. If you die then the team fight is happening while defile kills them all. So don't be afraid to die if the team fight is good.

Good luck in this build. It is good in the right hands.