First thing , i didn't make colorfull or put it in center of screen becouse is late and i
dont have time and is not really important!

Hi there , this is my first build guide so maybe is not perfect but i played Karthus like this and i'm happy with it...
Karthus is bringer of death , you don't know when , you don't know how but you will die...so let's talk a little about my style of play with him witch i call Kamikaze Karthus!

I think you are wondering why i picked Teleport and not Ignite so i will start with that.
This Teleport will help you with many things but your priority is farming and you need it fast there Teleport comes in , at some point in the game after you finish your mana or low health you need to go in base and you will lose some minions witch are important for XP with Teleport you make level 6 with 1 or 2 minutes faster (didn't really count but you will see) after 2 or 3 turrets down TeamFights will start and Teleport will help you get there faster.
Now my favorite thing about Karthus is ... he can start a fight (engage) go with e and when you are at low hp press Zhonya button for taking more damage after that they will kill you and then the show is on you can put a Defile for slowing them , leave Lay Waste alone you don't need it your oponents ask for a song and what better song then REQUIEM , if you don't kill them is not a problem becouse your team will and Karthus will be happy about it!

I hope you didn't get bored reading this and thanks your watching my build!