Hey, this is my 1st build showing how to have a good game with Karthus.
As playing Karthus i see that he can make a great damage. That withmakes you a big killer, you can make a team win in normal games and give some great aid in ranked games...
I think Karthus is a great AP champion, you can spam a lotand get every1 low hp withor kill runners.

Pros
- Great farmer.
- Good harasser.
- Awesome passive, which will grant you kills after you are dead.
- He can win teamfights, because he can do massive damage, even when dead.
- His ultimate makes him easy to get kills with.
- When he has his wall ready he can be hard to gank. Especially with(Flash)

Cons
- Very squishee and bad survivability, when wall is on cd.
- He needs to be fed, to be good in late-game.
- He is often focused in team-fights, which means you'll have a harder time finishing them off, after your death.
- Item dependant - If he lacks item, he will not do that big a difference in team-fights.

Death Defied (passive) - Upon dying, Karthus enters a spirit form allowing him to continue casting spells while dead for 8 seconds.

Lay Waste - Karthus unleashes a delayed blast at a location, dealing damage to nearby enemies.
Creates a delayed blast at Karthus' cursor position. After 0.5 seconds, deals 40/60/80/100/120 (+0.3) magic damage to each nearby enemy, this deals double damage if it hits only a single unit.
Cost: 20/26/32/38/44 Mana
Range: 875

Wall of Pain - Karthus creates a passable screen of leeching energy. Any enemy units that walk through the screen have their move speed, armor, and magic resistance reduced for a period.
Creates a 800/900/1000/1100/1200 distance wide wall at target location. Enemy champions that pass through the wall have their armor and magic resistance reduced by 15/20/25/30/35 and movement speed reduced by 40/50/60/70/80% (their move speed slowly returns to normal over the duration). The wall lasts 7 seconds.
Cost: 100/100/100/100/100 Mana
Range 1000

Defile - Karthus passively steals energy from his victims, gaining mana on each kill. Alternatively, Karthus can surround himself in the souls of his prey, dealing damage to nearby enemies, but quickly draining his own mana.
Toggle Off: When Karthus kills a unit, he restores 20/27/34/41/48 mana.

Toggle On: Drains 30/42/54/66/78 Mana to deal 30/50/70/90/110 (+0.25) magic damage to nearby enemies each second.
Cost: 30/42/54/66/78 Mana Per Second
Range: 450

Requiem - After channeling for 3 seconds, Karthus deals damage to all enemy champions.
After channeling for 3 seconds, Karthus deals 250/400/550 (+0.7) magic damage to all enemy champions (regardless of distance).
Cost: 150/175/200 mana

i use:
and
that because:
- at the beginning of the game Karthus has little mana and I use it enough to spam
- the Karthus is quite slow without boots and is also used when you want to catch an enemy that is running away with the spell(Defile)

optional spells:
- it's good to escape from ganks as i said before and you can be very hard to catch with it.
- It's a nice spell to use when you don't want that you're enemy escapes and saving you're ultimate to help you're teammates .

- +0.95 magic penetration;
- +0.055 mana regen / 5 sec. per level (0.99 at champion level 18);
- +0.59 ability power;
- +4.95 ability power.

- Increases your champion's critical strike chance by {0.66/1.33/2}%;
- Increases your ability power by {0.2/0.4/0.6} per champion level.
- Reduces the cooldown of your champion's abilities by {0.75/1.5/2.25/3}%.
- Your magical spells penetrate 15% of the target's magic resistance.
- Reduces the time spent dead by {3.33/6.66/10}%
- Increases your total health and mana regeneration by {2/3/4}%.
- Your ghost spell increases movement speed by an additional 8%, and increases the duration by 1.5 seconds.
- Increases your champion's mana by {1.25/2.5/3.75/5}% of your maximum base mana.
- Generates 1 gold every 10 seconds.
- Increases mana regeneration by {1/2/3} per 5 seconds.
- Your Clarity spell will now grant the same amount of mana to allies as your champion recieves.
- Increases your base movement speed by {1/2/3}%.
- Reduces your champion's cooldowns by {2/4/6}%.
- Reduces the recharge time of your summoner spells by 15%.

- +15 AP. +100 Health, +5 Mana Regen per 5 sec.
At the start of the game, this is a very good item for Karthus, because it has everything that Karthus need.
- Enhanced Movement 2. +20 Magic Penetration.
These boots are perfect for a Karthus since, give you more speed and spell penetration.


Then boots, you must choose one of the following three items:

or

or



- +20 AP. UNIQUE Passive: Your champion gains 8 AP per stack, receiving 2 stacks for a kill or 1 stack for an assist. This effect can stack 20 times; you lose a third of your stacks if you die. At 20 stacks, your champion's cooldowns are reduced by 15%.
- +50 AP. UNIQUE Aura: Gives nearby allied champions +30 AP and 25% Spell Vamp.
- +75 AP. +20% Cooldown Reduction, +12 Mana Regen per 5.


The next items to buy are:
- +60 AP. +450 Health, +525 Mana, Passive: Your Champion gains 18 Health, 20 Mana, and 2 AP every 1 min. Bonuses cap at +180 Health, +200 Mana, and +20 Ability Power.
- +155 AP, UNIQUE Passive: Increases Ability Power by 30%.
- +70 AP. UNIQUE Passive: Spells penetrate 40% of the defender's magic resist.

When I want to kill an enemy, my way to kill him is:

I use:
behind my enemy, activeand I spam with.


or:


When I see a runner with low HP I useto kill he (try not to steal your teammates :D ).