This guide is simple: Full damage.(My first guide^^)
I tried this guide for a long time and I think is the best build Kata can use.
There are many ways to play Kata..if u prefer u can increase magic pen. but it's actually useless ..or maybe u just prefer increase armor and magic res. ...however this amount of HP can keep u safe rly well.
If u keep 20 stacks of Mejara's u'll reach 900~ AP or more.

Same as before. Full AP..very useful in tha start game because it allows to start with 35AP(runes) + 20AP(tome).
However, u can olso equip Kata with magic pen.

Simple: AP<->HP.
Start with the tome->Mejara.
Is a good way to fed up faster tha others and if even if u kill or simple u make an assist u increase ur APs.
Rabadon's Hat is the base of the build..buy 2-3-4 caps depending on the situation.
I know that its effect is unique but this way u can contain ur amount of AP in 1 space of the inventory.
Warmog's is useful only for HPs: 1400~

Just because u start with low HP u need to deal some range dmg untill u unlock Shunpo.
Read more in "Team work"

The build is based on the matter of the start game..so u need heal and flash (to keep u safe under the tower after a shunpo kill, easy "rush").

Pros:
-Highest dmg of everyone.
-Best slaughterer in cracks.
-Fast Escape (Flash-shunpo).
-Full build + exp player = God.
-U can easy kill a nuker and equalize a tank.
Cons:
-U die easily if they focus u.
-70% of teams stun u to prevent death lotus so u just need to wait the best moment for the ulti.

U don't even need to jung. except if u need the last 100-200 coins.

This is the most important part of the guide.
If u are in a pre-made team u need to wait until a stun or simply an exhaust to cast death lotus.
Remember that Shupo skill teleport u behind the enemy so cast it ahead ur enemy to gain 1-2 meters to improve the dmg dealt by Death lotus.
The same works with a non-premade team but it's still hard..because u need to follow ur ally champion's skills(wait a stun or simply organize it in chat).

I'm sorry for my bad english, I hope u enjoy this ^_^