This is my AP build for Katarina, whom I just bought recently after seeing how many people were just decimating whole teams with her and the first guide I have written so please, constructive criticism. Most of my guide is similar to others, but I tend to buy items and pick skills differently for my taste. Any people that like this guide please comment and vote.

Pros:
Massive Damage output
Great skills
No resources, purely CD based
Clearly op

Cons:
Can be easy to put down with stuns/fears
Very squishy (most builds are)
Timing can be crucial

: For marks I go with Magic Pen because coupled with the Void Staff and the Abyssal Scepter, your attacks will go right through the other players like they were covered in paper.

: I go AP because with the extra power in the beginning, you'll really strike fear into your lane opponents.

: Dodge seals for a little extra survivability because the only other thing that you get is +hp from Rylai's.

: Again, AP Quints for even more damage early game leading for easy kills.

Albeit, I'm not very good with the mastery tree and I see it as very subjective. But for me and the Summoner Spells I choose, it suits me well. Just follow what feels right for you.

I choose and because at the Early to Mid Game, the other team tends to be able to get away when you don't want them. Plus, Ignite really helps for those heroes that heal too much i.e. and the like.

Early Game:
I start each game with Boots of Speed and 2x Health Potions . You can easily mid with Kat, but that's up to you. Most people will try to make you lane top or bot, but they don't know that either way is great. I don't try to go for the kill until either: A) They are really squishy or B) is up.

WARNING: Be aware of the heroes you are against, even squishy ones (Namely Fiddlesticks because he can fear you right out of Death Lotus!

Anyways, by the time you have enough gold (1235), go buy because if you do well, this thing will give you a serious punch and you want the stacks asap. Next fill out your for the extra speed and MP. Now your all ready to start wreaking havoc on the other team.

Start keeping awareness of the other heroes and see when you can pop in and kill a few. This will help your teammates by taking out one or both of the enemies in the lane, freeing it for a nice push. This is the time where you should buy the for the extra HP. Some guides say to finish Rylai's for the slow, but at this early all you really need is the Health.

Mid game:
Now is when you have to make a decision. You can either follow the guide and go for or . This really comes down to the game and how many stacks you have/still have to get. If your low on stacks, go for the Deathcap for the AP that you probably need. On the other hand, if you have plenty of stacks and have little to no trouble killing, go for the Void Staff to build up your MP. Of course, if you find that the heroes are being troublesome and not standing still to await certain death, complete for the slow and AP.

Late Game:
If you get to this point without already destroying their Nexus or the other team giving up because you keep killing them, then it's mostly a done deal. Fill out the other pieces of the guide (whichever they may be) and continue to further aggravate your opponents. And if you get so far that you need a sixth piece of gear, you could get a for the extra AP/-MP aura or a because it has all things that are good for Kat. Or throw caution to the wind and buy another Deathcap . (I once played against a Katarina that had 3 and was almost done a 4th by the time they won.)

Now, I take Bouncing Blades first because it's a great harasser and can allow you to get lots of last hits.

I then take Shunpo and then Killer Instincts .

Shunpo is going to be your number one go-to spell for Kat. It has a great range and instantly closes the gap between you and your prey, which allows you to Ult all over their face(s).

I pretty much only get Killer Instincts Rank 1 and then leave it until the end for its Active.

Then there's Death Lotus , this will be your killing machine. You poof in and then rofl-stomp the other team into oblivion. But be wary, as this targets the three CLOSEST enemies. So be sure to use this when there are only up to 3 champions in range otherwise your daggers will just fly around hitting random people. While that is good for the team, knocking down the Health of all the heroes, it won't get you those tasty kills.

Now for ganking, your rotation will be -> (for the DR)->then -> -> ->

This rotation is it. Basically you pop in on a champ with 35% DR and then throw your daggers at them. If they are not dead by that, then use your Ignite to put the nasty dot/-Healing on them. If they are still alive, which is really lucky, use Bouncing Blades to finish them or if you can, Shunpo. But be careful that you don't poof right next to another enemy, unless you have Death Lotus that is ;).

Follow this guide, and you'll have some of the most entertaining games you will ever play. So much so, you'll think about not playing her just to be fair (but you'll still play her, who are we kidding). Have fun and Happy Slaying!