Not Updated For Current Season
Early game, mid farm
Karthus needs to level up 6 fast, his ultimate Requiem can hit everyone. I even use it for kill steal...
with spamming Lay Waste you will get more creeps. Try to catch the enemy too. The combo for 1v1 is: Use Will of Pain to slow the enemy, use Flash and activate Defile.
Greater Mark of Magic Penetration is best for AP casters, it penetrates magic's resistance, so you're doing more damage.
Greater Seal of Replenishment . You need mana regeneration, for spamming Lay Waste.
Greater Glyph of Mana . More mana, more spam. You need mana for Defile too.
Greater Quintessence of Health . HP is for a little survivability, so in team fights using Defile you can survive the fight.
I get 9 points on offence, most important point is given to Archaic Knowledge . 21 points to utility, that means grows your Mana and your mana regeneration.
Karthus is a hard spell caster who needs a lot of magic penetration and ability power. So that's why i'm doing it. Rylai's Crystal Scepter is very important because it gives HP for survivability and slows enemies with your spells. Zhonya's Ring item is f*cked up so the new item is "Rabadons Deathcap" which give 155 ability power and increases AP by 30%.
Flash is important spell for karthus because he is slow champion and if he needs to run away or catch someone he'll use Flash. Flash is good for turret diving too.
Clarity. Karthus is spell spammer, so he spends mana. at level 13 i'm going to kill blue and get the blue buff which helps me for team fights because i'm using Defile which drains 30 / 42 / 54 / 66 / 78 Mana per second, so you wont be karthus if you dont get clarity or archangel staff.