This is my Karthus guide. As i focus on AP, you'll have to be very carefull. You will not have much HP, so it will be easy for your opponents to hunt you down. Therefore it is important that you stay with your teammates! if they tank for you, your team will be unstoppable becuz of your damage. with full build, i have around 1200 AP. Enjoy :D

I choose Magic Penetration runes so i can focus on AP in-game. you can also choose AP runes, but they'll only help you in the beginning getting fb. If you are playing ranked games, your opponents will be very defensive and try to gang you every moment, so you really wont have the chance to get some kills before you reach lvl 6.

To get a good start, i pick Doran's Ring, because it grants you life and mana regen. As a little bonus it also grants 15 AP so you really can harass your opponent with your q-abillity (Lay Wastw). AFterwards, Mejai Soulstealer is a must have if your team is doing well, otherwise you can pick haunting guise, again for extra magic penetration and HP. I prefer Mejai soulstealer becuz it rules! Then i start building up some mana, which will grant me AP later, and here is Tear of The Goddess an excellent choice, as it gives you 4 mana for each abillity used. Sorceress Shoes for MP, and do i have to explain why to buy Rabadons deathcap 30% extra AP? YES PLEASE! finish your build with 3 archangel staffs, and your game will soon be over. If you are playing against very squizy champ's (such as Teemo, Ashe and Ryze), your ulti will have enough power to deal them 3/4 HP.

If it is a very exciting game with lots of teamfights, and no team taking the lead, Zhonya's Hourglass is a great add to the guide (as last item). Use flash to get in the centre of the team fight, activate Defile, and use Zhonya's hourglass' active abillity to go into statis mode. with your Defile dealing about 400-500 dmg per second, you will be able to deal up to 1000 dmg in the time in statis, and giving you the opportunity to finish alot of opponents off with your ultimate. This should result in 5 dead opponents and a win to your team.