First of all, this is for some friends (thus for Blind Pick not ranked) and I am not sure with the skill sequence.(Lay waste should be maxed first).

This build is for "fast" casting of Karthus' ultimate to finish opponents, start a teamfight or just cause some trouble and chaos in the opposing team.

It is a so called glass/crytal-cannon (Etherion) build which means: 1% defense 99% offense.

You should go solo mid.

Pro:
- Massive damage
- "fast" ultimate

Con:
- nearly every well played stun/slow/whatever means death
- haters gonna hate


Don't forget that you can still cast for 7 seconds after death to get equalisation or even a doublekill.

Runechoice:
We are in need of less cooldown 'n stuff...

Alternatives:
Spellvamp/Abilitypower for better farming. (Selfheal/faster kills)
Manareg for an easier start.

Well... pretty selfexplaining:

Damage for damage.
Utiliy for cooldown.


Alternatives:
Slight changes in Utility if you personally like it better in any other way.

Just maxed out AP + shoes.


Alternatives:
1 Voidstaff when they push magic resistance.
1 Deathfire Grasp if you want even more cooldown.

Max out Lay waste as soon as possible. I personally like Defile better for mana-management but you can also use wall of pain for slowing and more dmg. (Again you have to decide for yourself.)
Requiem is priority 1 the moment its available but that should be clear.

Flash is the only defensive part in this build, flash out of aoe stuns before they happen or any attacks you see. On the other hand you can use it to finish off enemies with either defile or by placing lay waste infront of them.

Surge is once more a personal choice of mine, simply more damage.


Alternatives:
Heal to have additinal safety and to bother all enemies.
Ignite to deal some damage without wasting mana.
Teleport for.. bla bla

You know what all those Summoner Spells do and what their pros are, so decide wisely.

Put down wall of pain whenever the team starts to fight.
Use Requiem either to start or to end a Teamfight.
Stay in bushes to let someone else get aggroed first then go in and kill as many as possible. Worst case is some suicide action... but normally you kill at least 1 Person while you are dead.

Start farming Minions whenever you feel ready to get 'em all down within some seconds. (I just ignore the fact that you start "farming" right from the start when u are sololane.)

In mid-game (12-16) you can kill like all minions and neutral monsters within 4 seconds. (Buffs take a bit longer)

1. This ist for fun/random playing and was never tried in ranked.
2. You do not have any defense but high damage.
3. It's usable when you play alone (Blind Pick) but in teams aswell.
4.