Quick Tips To Turn Your Karthus Into A Murder Machine
Hi there, I main mid and I especially like Karthus 
. However I don't see him being played very often, and I think it's mainly because people don't realize how great he is. Right now Karthus is in a great spot: Not OP enough to warrant a nerf, but strong enough to dominate the enemy, and obscure enough that people don't always know what your abilities actually do.
The Build:
The first and most important thing to build as Karthus is a Rod Of Ages 
. This little purple stick will turn you into a death machine. Start out with mana crystal and potions, then then build it into Catalyst for the added sustain. Finally you should have a RoA between 9 and 14 minutes depending of your farm. RoA supplies Karthus with everything he needs, and is the perfect item for him. A Karthus without RoA is like an ADC without attack speed or lifesteal.
Next you should get you some 
Sorcerers Shoes for the Magic Pen and MS. Magic Pen is incredibly useful on Karthus.
My third item is almost always Rabadon's 
for the massive AP spike. Keep in mind while building this item it will be Karthus's slowest growth period, but it's well worth it.
The fourth item might sound odd to some, but it makes you nearly inescapable, which is invaluable because Karthus has no method of chasing down foes (Aside from his ultimate). I get 
Rylai's for the health and AP and especially the passive slow. The slow wins games, it turns literally everything you do into good CC. Wait wait hold on, health on a mage? After RoA? Yes!! I'll explain that later down in this post.
The fifth item I usually buy is 
Abyssal Sceptre for the huge Magic Pen and MR, but if the enemy is all AD and for some reason you don't need more damage, Zhonya's works well too. But it lacks the Magic Penetration Karthus values so highly.
Finally I purchase 
Void Staff. This item is really the icing on the cake, and makes you melt foes with even the highest MR. However if you're up against a bunch of tanks with HP but not MR, I might suggest 
Liandry's, as it procs well with Rylai's and while it provides less AP and Magic Pen, it gives a little health and the passive is excellent for just poking. Void Staff is the right choice 90% of the time, however.
The Abilities:
Q: A small 0.5 second delayed AoE bubble that deals double damage if it hits only one target! Late game you can 2 shot Akali with this thing, it's amazing. Did I mention it's on a 1 second CD??! Very low mana costs as well. However, watch your mana early game, it does deplete if you get carried away.
W: A spectral wall that grows in size and slow with each rank, but all ranks lower the opponents MR by 15% and slow, letting you cheese your way to an early kill. This spell costs a LOT of mana though, especially early on, and has the longest CD of your QWE spells, so use it wisely.
E: Ah, my beloved Karthus E. This spell is so useful, I would trade away my Q entirely for some extra E damage. E is a toggle ability, and when toggled on it creates a fairly large AoE around yourself that causes very nice damage per second to the enemy. Combine this with your Rylai's slow and your kills will skyrocket. Turn it on in a teamfight and use your health from RoA to survive while the enemy is dying just from being near you. Pop W and some Q's for added carnage. More on this later when I explain the passive. However this ability is extremely mana hungry, and even late game it will drain you like a popped balloon. Toggle it off immediately if you don't need it, you can toggle it back on again instantly. Also, when E is toggled off each kill restores some mana.
R: The Karthus Ulti... the ability that will make the enemy rage like none other... it really isn't all it's chalked up to be. At rank 1 it does 250 base damage, and only has a 60% AP ratio. This will rarely net you more than a kill or two every few games, but the threat of it keeps enemies recalling. However, at level 11 the base damage kicks up to 400, and you have a lot more AP by now, so you're probably doing around 530 with your ult. This is pretty good, and it only gets better. At rank 3, level 16, the base damage goes to 550... and by endgame you can easily manage 1000 damage with your ulti. OUCH, that HURTS!! Teemo's and Heimer's beware, this ulti can 100-30 a squishy opponent, if not more. Now the downside to this skill is that shields, especially Morgana's, will mitigate the damage greatly, and invulnerability from Zhonya's or an ability like Fizz pole hop will dodge all damage!! A tip for Zhonya's, the cast time for Requiem (R) is longer than the invulnerability lasts, so if they pop it before you start to channel you can kill them. Maw and Hexdrinker will also rain on your parade. Do not channel Requiem if you are alive and in a fight, death or any hard CC will break your ult and it will go on CD without casting. Run away or die before casting it.
THE PASSIVE: Karthus has one of the best passives in the game IMO. Upon death he gains infinite mana, and automatically toggles on his E. He cannot move or AA, but he can cast spells for free while in a ghost form for 7 seconds. KEEP IN MIND that your ultimate takes 4 seconds to cast, and if there's less than 4 seconds left in your passive you cannot cast your ultimate. This means that you can use Q twice (0.5 sec delay + 1 sec CD) and Requiem (4 second channel) once. If you're really quick you can get a W wall in there too. These 7 seconds count towards your death timer for respawn.
One last note, always know how much damage your Ultimate does. It's an awful feeling to blow your ultimate and have the enemy walk way with 30 HP. And if your team is saying "KARTH ULT!" don't just blindly listen to them. Make a quick judgement via minimap or screen whether or not someone can be killed, and then decide. They mean well, but often they're wrong. Consider sharing your ult damage with them when you get a new item or rank up. Also, while some might think Karthus Ult is best used as an initiator, I fervently disagree. If you ulti to initiate then the enemy will be weakened, but there's still no guarantee of a kill or even that your team will win or even needed the extra damage to win in the first place. There are situations to initiate with it, I'm sure, but I have yet to run into one of them. You can call it greedy, but I'm not going to ask an ally to ulti someone at full health so I can kill him either.
Did I miss anything?
