This is strictly an item build, Its based off of "Your AP Katarina Du Couteau Resource" but I choose WoA over Gunblade for three reasons, its cheaper, if a teammate gets it the auras stack, and the life steal/AD of Gunblade is less useful on an AP character. I reordered some things, this build in comparison to "Your AP Katarina Du Couteau Resource" will give you better AP with a different survivability based off magic damage primarily, picking up belt a bit later.

Remember Abyssal/Void Staff is a choice based off the opposing teams magic resistance. A big part of team fights is focusing down their DPS, abyssal helps doing this by reducing M-Res. on surrounding enemies instead of just effecting your damage. If the majority of the opposing team picks up more than 40 M-res, void staff will now be more useful (FOR YOUR DAMAGE ONLY) so if you are the only AP user get void.

Don't fret! This is very simple. Start off your character with bouncing blade instead of Shun po. So your initial skill order will be Q E E W then continue with your skill as posted above. Be weary of champions like Vayne or Ashe. If you don't know what you're doing against them. they will wreck you.

If you happen to start off doing extremely well a.k.a you are dropping enemy champions like flies you should pick up a Mejai's this will seal the deal on this character and you will have 900+ AP when you have all the items in the build. keep in mind if you make a Mejais you're going to have to skip out on your Will of the Ancients.

If however you are not getting the push you need in your lane and you're not doing well. You should focus highly on getting AP so you can take care of your lane.

When you're by yourself against an enemy champion first you must analyze your target.
for example: Annie is by herself you see all the enemy champions on the map. Start off by lowering her health by using Killer Instincts Followed by a Bouncing Blade. when you see her health drop about to 45-50% it is now safe to Shunpo in and cast a death lotus or just another bouncing blade for a kill. However if you're laning against Cho'gath Harass him slowly with your blades and only jump in when you know you can secure the kill. Remember, He's a tank and if you use your whole death lotus on don't kill him. he's probably gonna get away from you and if the other player is ANY good. he just dropped your health so now you have to Recall and waste time and experience.

Playing as Katarina you are VERY IMPORTANT in team fights. If you do not do things right ten-to-one your team is going to flame you and scream at you so do things carefully and intelligently.

In a team fight you can DEVASTATE people as Katarina. when a team fight engaged you're going to want to cast a Killer instinct followed by a Bouncing Blade into the enemy champions. If you have good AP you will notice it does pretty hefty damage. it also give the champions that it hits 50% healing reduction. keep harassing with this until you see the dps characters life bars starting to go low. this is your time to shine. Quickly use your Killer Instincts and jump in with a Shun po followed by a release of a very devastating Death lotus.

Laugh as you watch the opposing team rage because you just scored anywhere from a Double Kill to a Penta Kill provided you did this correctly.

End game you're going to start realizing that you are built like a cannon. This build gives you 594 * 30% which is 772 AP. You're tough but not too tough! play it smart like always but realize that if you run into a Fiddlesticks or an Annie or something of that sort you can pretty much exhaust them and shun po to death lotus and laugh at how fast you drop them.

Jarvan
Garen
Renekton
Xin
Lux
Morgana
Vladamir
Malphite
etc..

Your main priority is to lane with someone Beefy and Tanky. Katarina is EXTREMELY squishy and if you're laned with another squishy character. switch lanes with someone or your lane is going to get owned.

Avoid at all costs laning with squishy characters. I CANNOT stress this enough
For example:
Fiddlesticks
Soraka
etc..

Early game Katarina is a weakling. period. you want someone to nurture you until you can get out there and start destroying. try not to lane with other weak characters and you will find that your games will start alot better.

I learned how to play Katarina using this build:

http://www.mobafire.com/league-of-legends/build/your-ap-katarina-du-couteau-resource-dont-play-with-knives-61072

I have modified it and have noticed i've been getting more kills.

My thanks goes out to wRAthoFVuLK for the build that I learned from.

and Cagg, Thave, noldevin, bloodybuddy, and sturdyhammock for teaching me how to play well with Katarina

Have fun and hope to see some of you using this build in game.