Katarina is melee mage and assassin.I think that she is one of the best champions on mid lane.When I am playing Katarina on mid, I am beating champions like: Orianna,Cassiopea or Syndra pretty easy.
Only with Brand,Le Blanc or Ahri i have problems , because they can counter Katarina pretty well.And Katarina is very good for gangs other lines.When i get lvl 6 i ussualy go gang others lines and probably i get kill or doublekill.Get a doublekill when i go gang is not so hard because katarina's passive reduces cooldowns by 15 seconds , so combination + + sinister steel deals so so much more damage and when kill someone or assist these abilities has been refreshed.Katarina can escape pretty well too , because you can use shumpo on champions in your team and port on them (also minions,wards..)
When you feed Katarina , Katarina can win a lost game because her ulti is pretty OP :-)

EARLY GAME

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Boots of speed and 3 Health potions
I always start with these items.Boots are good on gangs/escape/faster gangs/mobility and potions are good everytime.


Sorcecer's shoes
Gives you magic penetration and movement speed.


Liadry's Torment

This is a good item for Katarina.It gives you pretty good nubmer of ability power and health its important for Katarina because without health is Katarina paper.So this item very good for Kata and i am building it in all of games.


Deathfire Grasp

This item is good for Katarina as same.It gives you nice number of ability power and Cooldown Reduction as same.Its very good item to early game.You can build it like first item after Sorcerer's shoes.So i think very important item for Katarina.

Late Game




Rabadon's Deathcap

Its great item for AP heroes.It gives you so many AP + increased all AP by 30%. Its important item for Kata as same , i am building it in all of games, because my damage is so so much better.



Void Staff

This item is very good when enemy team is building Magic Resist.Because your damage is still very high.I am building it very often.Its good item for Kata.



Zhonya's hourglass

Very good item in late game.It gives you nice number of AP and Armor as same.It very good when the enemy team focus you because when you activate item you give a vital for 2 seconds.It can be a last item.Very good for Katarina.



Abyssal Scepter

If you need more magic resist go for abyssal.Its good for defense that you will not toilet paper :-)



Rylai's Crystal Scepter

You can also go for this item, i am building it very often because it gives you nice number of AP and very important health (500).Its good item for kata as same.

Vocarity

I love this passive.If you get kill or asist all of your spells are reduces by 15 seconds. its just great.So dint be scared use ulti fo 1 champion because if you will kill him or asist you ulti will have cooldown only 28 seconds. its great.


Bouncing Blades

This ability is amazing for farming/damage in late game, when is enemy team in group you can hit all of them and deal pretty nice damage.

sinister steel
Sinister Steel

I love this spell.Very very low cooldown and very nice damage , kata hasnt mana so this ability is amazing if you combinate it with so it deals mega damage and if you use ulti after that you can instakill almost every champion.


Shunpo

This is great for escaping/ganging/chasing.. just very good ability because you can port on champion,wards,minions just great.


Death Lotus

This ulti is perfect.If you jump to the teamfight in a good moment and use this ulti you can get triple kill minimum.and if you use ignite with ulti its pretty easy kill.it deals damage to the 3 nearest enemy champions and its really good damage. with your passive you can kill everyone in teamfight because you passive reduces cooldowns by 15 sec after all kills or assists.
Great ulti.

There is some of my games with Katarina with this guide