This is the most anal Build I have ever used to play with Karthus, which I got from watching a member of CLG or SK play during the 2011 Dreamhack qualifications.

I never thought the concept of Exhaust would apply to Karthus, soon I realized the fun of walking right behind a fleeing enemy and bombing him with unreal Q damage for easy kills.

Another concept I did not this would apply to Karthus was Hextech Revolver. The spell vamp is very true for Karthus. The AoE of his E along with bombarding Q makes him regenerate his health faster than he is loosing in IN THE MIDDLE OF A TEAM FIGHT. not only does he NOT DIE, but he gets the Quadra from his AoE alone, which is a real pain in the *** -_-

I'm not here to teach you how to play Karthus, you can learn from a more professional Karthus Build.