I have almost a primarily ap rune book this adds a lot of damage with you're q early game and with the addition of rabadons deathcap its a even better chunk of damage. With these runes I can also afford to go tankier early game. To capitalize on these runes I farm and avoid harass while laning until about lvl 5 or 6. The reason i start at 5 is either there still not playing passive because there afraid of my ult or I want them to be afraid of my ult. At around lvl 5-6 the ap from the runes really starts to kick in. You want to wait for the creep lines to collide than try to land you're wall on them or just behind them. The magic resistance debuff on the wall combined with extra ap from runes will allow you're q to hit extremely hard. Since the creep lines collided you shouldnt have too hard of a time landing lay waste. Sometimes you can circle around to the side of the lane so you can change the angle of the wall to make it so if they run in a straight line they take the full duration of the wall (most wont do this). If there smart they will leave the wall before running to the tower, if they do this they are still running a longer distance because now they cant run in a straight line. Another wall trick that works better at solo top is purposefully missing them while placing the wall behind them and at a diagonal, this is good at top against opponents that like to hug the bush. If you block half of the lane they will either have to run though the wall where you can hit you're lay waste or they will run the long way around the wall giving you plenty more time to hit them even more. It is important that you get good at landing lay waste. If you are not good at landing lay waste they will proceed to play agressive back on you.
Starting items: dorans shield helps with lane dominance against ad solo's and to help sustain you're lane. Or sapphire crystal and 2 hp potions are good if you want a quicker start on your build and you are not concerned with being out harass. First back: Try to get these items on first back they will help you sustain you're lane and keep you're mana and hp up while you farm up you're next items Core items: Rabadons and void staff are core items rabadons for the massive ap and void to counter the enemies magic resistance. Void staff is listed as a core item with the assumption that they WILL get magic resist. If for some reason they dont get magic resistance than this item can be replaced. When determining the item build that is right for you look at your team. If you're the primary source of ap than you will need a more ap heavy build. If you're team already has damage but you are lacking in the tank area you can prob afford to go more defensive early game. Also does you're team have plenty of cc to prevent people from focusing you? Also look at there team composition. Who will be focusing you during fights? Build option 1: Typical build good ap throughout the game with defensive items for the end game Build option 2: against heavy caster team. Either after finished rabadons or need rod than upgrade catalyst into a banshees Build option 3: tanky dps diving into you every fight. If they are already stacking magic resistance before you finish you're rabadons than delay the deathcap for a earlier voidstaff The longer it takes for the enemy to focus you the more damage they will take. If they stand in your aoe while hourglass is activated they are taking meaningless damage. If the effect wears off and they kill you more than likely with the use of you're passive you can ult and mop up. Items as karthus are very situational. Get what you need as you need it but dont sacrifice too much ap. You are still a caster not a tank. OMG but karthus is a R button and he needs soulstealer - the answer is no. There are times that soul stealer can be effective. You get soulstealer when your team is WTF slaughtering. When your behind but you need that one team fight to put you back in the game. When you are doing GOOD and you have strong aoe team that is already ahead. If I had a good start and my team is looking good than I might get a soulstealer to snowball my teams lead. -Just keep in mind that soulstealer can be risky and you will probably get focused during fights so you are at high risk of losing stacks -With snowball items just because you can doesn't mean you should. Just because a situation above happens doesnt mean you should include a soulstealer. Yes in the build you wont be as squishy and you can get stacks on soulstealer while dead but you will still be a primary focus because of you're insane damage
Lvl 1-4 last hit and avoid harassment Lvl 5-6 while still last hitting try to take time to be agressive (wall lay waste combo)
Farm when you can, try to always get blue buff. Karthus is also a good ganker. Wall first so they cant run and land those lay wastes. When you're team does dragon you should be helping them. Karthus can dps down dragon very quick with lay waste and the help of his team and if you're team gets caught you're wall will prevent initiations. Karthus also has insane team fight presence.
If you're team goes for baron its pretty much the same thing as if your team went for dragon. you're lay waste can dps baron down pretty quickly and save you're wall for if there team comes.
If you are a part of an aoe team composition get in the middle of the fight with that massive aoe. Stick close to your team. I like to stick close to my teams ad carry so when the enemy focus is my ad carry I can wall them away and defile drain there hp. If you are not being chased or focused go straight for there carries try to get good lay wastes off and scare them away from the fight. When you are being focused try to get the enemy to chase you. Make good use of you're aoe. Leave defile on as you flash away than ghost, and finally activate you're hourglass. As a karthus I dont want to get away I want to run away but i want to go at a pace where i can keep them chasing me. I would rather than try to kill me than my teams ad carries. Also when you die make good use of you're passive defile there team lay waste and finally ult before you're passive ends. Karthus is really strong when fighting in the jungle because with a good wall positioning the slow is unavoidable so they wont be able to escape you're aoe.
The reason I choose to max Wall of pain over defile is because of the magic resistance debuff. Early game that debuff is enough for insane damage combined with runes. Defile is a really strong aoe damage which is good late game, but early game when you are trying to solo a target the magic resistance debuff is way more effective.
get to a safe place where you cant be disrupted by a silence or a stun. Wait till you are dead so you it doesn't get cancelled mid channel. Also karthus is really good agaisnt "diving" champions such as shaco. If a shaco dives onto you activate you're aoe and when he blinks away with no hp ult him.
Huge slow, Good magic resistance and armor debuff Use you're wall to prevent ganks, prevent enemy initatiation. If its a stand and deliver fight use you're wall to amplify you're teams damage. While fighting in the jungle you can position you're wall to fit the entire path way length wise not just across this way the enemies are forced to walk though the full duration of the wall.