Hello this is my first guide and am very happy to introduce my knowledge about my favorite champ Kat.
AP Kat is the only viable Kat there is. I do NOT want to make this Guide very long with double spacing or anything fancy. This guide has all the essential without all the pretty stuff in it. Although criticism is welcome please don't ask for pictures of the item or anything like that thank you.

Top Kat consists of the same items just that you get Armgaurds instead of Needlessly large rod because of the sustain against a AD TOP.

Pros
-Passive reset on her abilities
-Spamable spells/no mana
-Her shunpo's utility let you get out of ganks chase and maximize damage due to her resets
-Great Bot ganker(usually a double kill)
Cons
-Interuptable ult
-She is just Damage no CC
-Focused if not carefull
-HAS TO PICK UP A KILL/ASSIST FOR RESET

Her Q passive then W to pop the Actives on kat lets her easily farm her lane. This can also be used to harass the enemy laner by Q'ing them you have put the Q passive above their heads. Then by W'ing you will activate the Q passive. You can also just harass with your W and run away because of the movement speed boost but you will need to remember your W borders

The only thing I would change in the runes is the AP quints to Movement speed if I was in high elo because in high elo they wouldn't stick around in lane for you to kill them. So really the AP quints in high elo would just add easy farm rather then the ability to gank bot faster or have some doors open if you are chasing.

First considering a gank first comes when you have pushed your lane and your enemy laner has B'ed. Ganking comes with a smart outlook on a situation. If you are going to gank you will not always need to use your shunpo. You could use it as a tool to catch up once they pass you because most likely they will run past you when you ult. If you're going to gank bot then you will hopefully see that they are pushed up or have low health (but thats a different gank situation). So bot lane is pushed to your tower. You go bot to gank because your jungle is ganking top lets say and well you will want to just run into their walking path and ult when your in the way but be careful because the support might have an interrupt CC which you should ping so that your teammates can initiate and they support will most likely use that CC. Once you have ulted and they are at the edge of your shunpo then shunpo onto then Q them for the damage and the Q passive then W and you should then follow with kiting because your W activates the passive and also gives you momentary movement speed. Once you have killed one then you should get a reset and then shunpo---->Q-W----> KITE the second bot enemy champ

If ganking bot with low HP

Main Items

Sorcerer boots are there because of the Magic Pen. AP mids need this item early/mid game for the added harass.

Zhonia's hourglass is there because of the utility/AP of the item. The fact that you get focused alot in team fights and because you have to shunpo in to use your ultimate comes with the chance that they will focus you because they are right next to you which leads to you dieing. Having this item helps because it not only gives you invincibility but gives you the time for your teammates to kill your enemies because they are trying to click on Kat when your in Zhonias and gives some time to you.

Rabadons Deathcap is essential because of all the AP you NEED.

Gaurdians Angel needs to be in this build because you get survivability from this item aswell as a second chance to live. This plus Zhonias gives you enough time for your shunpo to reset and to Ward Jump out in order to survive.

Liandrys torment this item makes this build great because its and mid to late game item. The passive on this item is what makes this item. This item is 5th because usually the enemy team has stacked alot of HP which this item eats up.

Void Staff (Penetration Stick)is last because by this time because the enemy team has stacked MR because you are getting so many kills they have to counter you.

The build order can be change from the boots/hat/HG and also can be changed in the Liandrys/Void Because they come with countering the enemy teams build if they stack hp against you then definitely get Liandrys 5th. If they stack MR then get Void staff. The boots situation comes with a bit of experience. I usually end up getting rabadons then Boots then HG but sometimes I got HG then boots and then the Hat. Its all depending on your teams situation and if your winning or losing. The HG is a huge game changer and Rabadons can easily snowball you into winning the game.

Situalional Items

Mejais soulstealer is an amazing buy for Kat replace it with liandrys and buy it first if you wish to add ALOT more AP. This comes with danger though, because you have this item the enemy team will respond with giving you no mercy but usually land your team a few seconds because they will focus you like no tomorrow.

BAD ITEMS
Deathfire Grasp is a very bad item for kat. Other then the extra 120 AP this item is trash to kat. The % damage from the passive is covered by Liandrys and the extra %20 Cool down reduction is not needed because of Kat passive

I usually go Flash/ignite but sometimes depending on the champion I go exhaust because of the extra debuff. The ignite is also there for the extra buff and also the extra debuff on champions who heal relatively fast like Dr.Mundo

Your wards can also be used for getting out of a sticky situation. Her shunpo onto a ward can help you have a second flash. Which is why smartcasting is essential for Kat. You hit your ward and immediately E onto it. This is also good for jumping over walls which could also help you stay alive. I have my 2 and E smartcasted for easy ward jumping. On Kat always have at least 2 wards on your person. 1 is for putting one down to not get followed and the other is for your shunpo ward combo to disengage.

In team fights DO NOT INTIATE. In team fights you are not the tank. You must wait for your team to initiate then wait for some/ALL CC's to go off. As you wait throw your Q in there. Then when you see an opportunity go for the ADC or AP which ever is easier/closer/squishy. You shunpo on to them W or just Ult and you should have to CC to interupt you and they will attack you but you will finish them off. When your have killed one or two shunpo/Q/W them all until they are all dead. If they focus you then just pop your Zhonias wait and if your team is losing then disengage and RUN AWAY.