The mentality of most people when playing karthus is to not worry about dying. They get what i like to call Tryndamere syndrome. Lots of people see Karthus's passive and think hmm if i can continue attacking after i am dead then i guess i should just be squishy and go in die and continue attacking. I have found that this is a dumb method. You get lots of kills and lots of assists but you also get lots of deaths. With my build you will be a Karthus who runs in and attacks with his AOE to take a team down and then if he dies he will kill everyone else with him.

Many people will not like my build. They will complain about not getting tear drop into an Archangel's Staff or about my skill sequence. I hope i can calm your doubts and show you a good Karthus build.

Pros

High ability power damage
Good survivability
One of the best slows in the game

Cons

Squishy early game
Slow Movement

The first item i get is Mana Crystal. It gives you enough mana to stay in lane long enough to get your farm going. Here i go a different route than most Karthus builds do. I take a Catalyst of the Protector. When i first started out with Karthus i would always go tear of the goddess here instead of catalyst because i always ran out of mana. That's where your skill order comes into play. By maxing Lay waste and defile equally if you make sure to last hit you will not run out of mana quickly. The main reason to get catalyst is the extra health. Early game your lay waste and defile do enough base damage that you don't have to worry about getting AP items to be effective. Also the bonus heal and mana regeneration from the catalyst are nice.

Next the mercury treads over boots of lucidity. The only spells that boots of lucidity would help with are Wall of Pain and Requiem. With this being your only CD reduction item though it wouldn't help a whole lot. You would be better off just getting blue buff and Elixir of Brilliance.

The rest of the items i find to be pretty self explanatory. Deathcap so you hit uber hard. Will of the Ancients for the spell vamp. Rylai's Scepter for the health and the slow, the slow makes it so they cant run out of your AOE if you are chasing them. And last but not least Zhonya's Hourglass. This is a good item for Karthus. You get 100 AP and 50 armor, as well as the active ability that allows you too be untargetable for a short amount of time. The great thing about that it your defile continues to do damage the entire time.

The only variation i make it if they get magic resist then i will get abyssal scepter instead of Zhonya's.

Please let me know if there are any changes you want to suggest to me for this build. I would love to get feedback from you about my build.