Hi...

Here I'll show you my build/guide of katarina...
this guide, combined with a decent player skills can and will be the deadlyest build ever.

ok...end of talk...lets get to action...

I use 9x Greater Mark of Magic Penetration, 9x Greater Seal of Scaling Ability Power, 9x Greater Glyph of Scaling Ability Power and 3x Greater Quintessence of Scaling Ability Power becouse katarina doesnt need armor, health, magic resist and much less mana...
So there are no reason to use other kinds of runes with her...

I take 9/0/21 beouse that is what an ap carry (with no mana) should have...

Many people ask me with not some defense masteries...

I just anwser this: becouse are tanks to have it ^^ (jk)
I say it is becouse CD is everything for kat...so you can have your 9% of CDR at lv 1 with this strategy...

First I start with

Doran's Shield. (But Kritous.... why dorans shield?? why not Boots and 3x Health Potion)...
¬¬' look: i tested many times every time i did NOT buy Doran's Shield....if i needed to dive lv 6....I killed the guy...but I died too...so no worth it...the 120 hp doran's shield give is awsome and you will see if you dive with doran's....you will leave the turret range with something aroud 70 or less hp...

After that I rush Hextech Revolver. Why? 15% spell vamp give you much more power in lane.
PS: just go recall after you have 1200 gold....(1350 better...becouse you can buy 2x Sight Ward together...) { Vision Ward just in case of Evelynn or Shaco}
After that some speed need to appear...but not too much for now ^^ so just grab ur Boots

Now big question ?????
Why not Mejai's Soulstealer ?
I just recomend it if you can get 3 or more kills on mid lane BEFORE some turret go down

Moving on we get the Rylai's Crystal Scepter starting with Blasting Wand (860g)...but if you feel like need some hp...go for Giant's Belt
Rylai for katarina is every thing becouse with its slow...people wont be able to leave your Death Lotus (ultimate) area so easly...they will probably need to Flash or something like that..

After rylai I follow up to build normally...( i dont think any1 got questions about the further itens)

As my last item...i searched a lot... and i got the final ideia of...4 topics

1: Game easy and not much deaths? --> Second Rabadon's Deathcap
2: Game easy but getting focused? --> Guardian Angel
3: Got a karthus in game? --> Zhonya's Hourglass
4: (not much used) got a Malzahar ulting you? --> Quicksilver Sash

Ah! Here comes the cool part...

:: (First Skill): MAX IT AND ABUSE IT....
Honestly I confess...until lv 5... don't be scarred of being a little pushed... NORMAL... your bouncing blades doesnt hit so many targets... But from lv 5 and on...have fun with your enemy...

I'll leave killing instincs for the end... (complicated for some)

:: Awsome chasing skill, with tremendous dmg! Used for last hitting creeps and avoid skill shots (such as Javelin Toss from nidalee)

:: OMG! That's what katarina is made of! there would be no Kat if that ult didnt existed!

AH! passive skill! 25 gold PLUS 15 secs of cooldown reduced if an assist or a kill happen...
That is the reason Katarina can Triple, Quadra and Penta Kills

:: For laning fase... lv 1 is enough...this skill is really awsome... it can lead where the fight is going (to your kill, or to your death)
I'll give exemples: better to explain:
1) Fighting Vladimir (super normal):
He heals alot! so you want to reduce that so you can have some chance right? killing instincs allow u to do that...if u use ur W skill before using Q...your target get his healing/regeneration effects cut by half... You are good then to kill vlad...
So ur skill sequence should be: Q, W, E and R
Beware!!! vlad can sanguine pool...so be ready!

2) fighting Teemo (normal too):
If u W before E...you get -15% dmg for some time...who doesnt want to get less hit??
Here the skill sequence should be: W, Q, E and R
no trouble here....he might flash or something...or for ur happiness die ^^

Enemies you shall rule over:
Teemo, Malzahar, Lux, Ashe, Ezreal, Twisted Fate, Heimerdinger, Karthus and Orianna and some more

Enemies you will be careful about:
Katarina, Akali, Kog'Maw, Veigar, Ryze and Anivia and some more

Tough Enemies you want to be REALLY CAREFUL:
Brand, Vladimir, Annie, Caitlyn and Vayne

Favorites:
Ignite....dont u hate when some1 escape with 50hp?? Be fast and dont let that happen again!
Flash.... cool escaping routes and some cool tricks to do (later shown in ss)

Can be Used:
Exhaust....cool against dps...and mages too, recently ¬¬'
Teleport....ya might be a good ideia to save some turrets and to gank but... idk ^^
Cleanse....not bad but not good ^^

DONT USE!:
Fortify: let for tanks
Clarity: Kat doesnt use mana...she uses....nothing!
Clairvoyance: let for support
Revive: U not suposed to die!
Rally: barelly no1 uses it...u dont use too