Welcome to my Katarina AP build. This build focuses on giving Kat a bunch of AP with some survivability included. Kat has wonderful Abilities that synergize quite nicely and her Passive makes taking down the enemy team simple. If you like what you see, try it out. And don't forget to comment/vote at the end.

Marks - Magic Penetration
Seals - Dodge
Glyphs - Ability Power/Level
Quints - Ability Power/Level

Since Kat's spells deal magic damage, you want Magic Pen Marks. The reason I choose Dodge Seals is more of a personal preference, because if I'm having issues surviving then I switch out my Sorcerer's Shoes with Ninja Tabi. And AP/Level Glyphs and Quints will give her a good AP boost early game to score some kills and even more later.

Obviously, you want extra Magic Pen for Offensive Masteries. In Utility, since Kat has no Mana, don't get in points in things that affect only Mana. I feel that this part is pretty self explanatory. Things like Cooldown Reduction and extra Movement Speed will really assist in getting kills.

I always start out with Boots of Speed and 3 Health Potions. I need that Movement Speed boost early to start harassing the enemies. Then, I upgrade to Sorcerer's Shoes for added Magic Pen and grab a Hextech Revolver for some Spell Vamp. Then, Rylai's Crystal Scepter for extra AP, Health and Slowing. The slowing effect will help keep enemies within range of you Death Lotus longer and is overall insanely useful. I then grab the Mejai's Soulstealer to start building my stacks. Next I grab the Abyssal Scepter for AP, Magic Resist and aura of decrease Magic Resist for enemies, making Death Lotus even more potent. After that, a Rabadon's Deathcap to really boost my AP. Finish off by upgrading the Revolver to a Hextech Gunblade.

A quick word about the Soulstealer. At a full 20 stacks, this item gives 180 AP. With the Rabadon's Deathcap Passive bonus, this is then boosted to 234. In comparison, a second Rabadon's Deathcap will give 202 AP. The Soulstealer also gives 15% Cooldown Reduction. And it only costs 1235 gold. A soul-stacked Kat can carry a team. Never underestimate this item. But if you're having issues keeping up the stacks, sell it for the Zhonya's Hourglass and sell Sorcerer's Shoes for Ninja Tabi. The hourglass gives extra AP and Armor and Ninja Tabi will increase Armor and Dodge chance to 18.75, making almost every 1 in 5 attacks miss.

Passive: Voracity - Kat gains 25 Gold and 15 seconds reduced from all Cooldowns for every kill and assist. This is among the best passives in the game. If you manage to get two kills with her Ult, you can fire off another Ult within seconds.

Bouncing Blades (Q) - Kat throws a blade that bounces around nearby enemies, dealing less damaghe to each one it hits. This is a great harassment ability early game as it is her only ranged attack. It's also good for farming, which is why I upgrade it first. When used with Killer Instincts, the blade deals full damage to all targets and gives reduced healing effects.

Killer Instincts (W) - Gives bonus damage to Abilities and Melee. Also gives a bonus effect to the next use of either Bouncing Blades or Shunpo. I put one point in this at Level 2 to allow myself to get these bonuses, then wait to finish upgrading it until the end.

Shunpo (E) - Kat teleports to her target, and if it's an enemy she deals damage. Kat can use this to keep up with her fleeing targets as well as escape by teleporting to a nearby minion or friendly Champion. When used with Killer Instincts, Kat takes reduced damage for a few seconds, a perfect setup for her Ult.

Death Lotus (R) - Kat throws up to 10 daggers to up to 3 nearby enemy Champions over 3 seconds. Kat has to be near enemy Champions in order to use it. So, by using Shunpo to get next to them, a quickly followed Death Lotus will do serious damage. In the beginning of the game, it's best to use this to finish off enemies. Near the end, though, it can take out those squishy carries.

I go with Flash and Ignite. Flash is good for chasing and escaping and, combined with a Shunpo, is a fast way to get in position to fire off a Death Lotus and Ignite gives extra damage.

Early Game (1-10)

In the beginning, focus on harassing enemy Champions with Bouncing Blades and getting last hits on minions. If you're soloing, don't go for the kill unless they make foolish mistakes and stay too long, but wait to get Death Lotus. After that, you can afford to take some risks to get kills. If paired with a good partner (one of my favorites is Blitzcrank) you may be able to manage kills before you get your Ult. Work with your teammate and play smartly.

Middle Game (11-15)

By now, if you have managed to take a turret, feel free to assist in ganking lanes that are having trouble. Although Kat has no way to stun or slow without items, she can deal heavy damage and excels at chasing those who run with Flash and Shunpo. However, you need to balance getting kills and assists to build Soulstealer stacks with surviving to maintain them. Getting a kill for two more stacks is not worth dying and losing even more.

Late Game (16-18)

It's time to have fun. With Death Lotus maxed and several AP items under your belt, Kat can massacre her enemies. Work with your team to push and pay attention to enemies who get stunned or if the other team commences a fight and ignores you. Shunpo in and activate Death Lotus to destroy them. Once you near 20 stacks, beware of getting focused by always having an escape planned.

Kat is best used as a surprise attacker. When the enemies start a fight they think they can win, Kat using Shunpo and a Death Lotus kind of ruins their effort. It's best to push and destroy turrets with your team, but that doesn't mean you can't take a turret without them. Go with a large crowd of minions and keep an eye on the map. If you don't see a few enemies, plan an escape in the event of a gank.

When well played, Katarina is lethal. Having no Mana, strong Abilities and a Passive that shortens their Cooldowns by getting kills and assists, she is among the best carries in the game. Try out this build, vote and leave comments/critiques/suggestions. Blood for Noxus!