Well you all know katarina and you all probably whined about her ulti and having no interupters in team (i was one of them before i tried her) but have you even tried playing with her?
I actually hated her the most before i tried her once and then fallen in love with her. Why?
Becouse she is actually easy to play and has a lot of dmg, she can be hybrid ad/ap (wich i play but having more ap then ad).
You depend on your and the enemy team(well on most champs but on kata definetly the most) becouse if you dont get your ulti in you dont do lot of damage and your team has to be good and defend you while ulting by shield or taking them off you. If other team has silencer (fiddle) or a stunner (sona, veigar...), you should wait till they throw stun/silence and then ulti or you will probably die if you get silence.

Well about runes i actually recommend the potency marks, seals and glyphs and quintessence of insight but I actually don't play with any specific runes for her, so feel free to take any other runes.

Masteries I think are the same for all ap champions similar to katarina and there isnt anything new with it. Probably people will be freaking out becouse atack speed and damage but i puted becouse 2 reasons: first you need to take some towers too xD and seconde well didn't have anything useful to put in offense :D

This is what i use and it deals pretty much dmg with bb and ulti becous ad and ap stack on those 2.
Yes i know i should've putted da mercury treads for stun/silence duration lower but i like it more with mp boots.

It goes with my items. I am maxing paralelly bb and shunpo to get max burst of shunpo bb ulti wich is usually at least 1 kill if you dont get silence/stun.
As you can see i gave shunpo lower dmg bcos i use it more to get closer to ppl so i bb and ulti them then to actually deal big dmg.

Flash is always useful to run away when noone to shunpo on, and ignite for 10 additional ap and more dmg.

Katarina's all skills are actually unique. Yeah i know fiddle's got similar spell to bb and it is better bcos it silences. But all others are unique. No champ can update their spells to reduce healing/damage taken. No champ can teleport on enemies *** or tele on his tm to run away, and no champ has channeling ulti with so many damage and so many ppl that it shoots.
NO champion gets more money and cdr for kills and assists(yes i know tf's passive but this is smthing better)

This is something you CANT DO. NEVER, NOWHERE, NOHOW. Katarina is probably the worst jungler, and i haven't seen any1 play jungle kata so stay away from it.

Well more or else that's all. Most ppl will call me wierd for this build becouse it's not usual to play katarina like that but that's how i play her and i actually do good.