Hi,

I'm Pallis123, a player on the EUW Server. I'm just bronze IV, but I think I play Katarina quite well and wanted to share my ideas with you. (And if my idea's are good it doesn't matter I can't play, right? You can still use them :D) This guide is a combination of Scarra's and TiensiNoAkuma's playstyle. I hope you enjoy it!

Pros + A lot of damage + Fun to play + The best clean-up fighter in the game + Possibility to make insane plays + Snowballs very hard

Cons - Melee - Squishy - Focused down easily - Is useless in terms of crowd control - Hard to play

• Greater Quintessence of Ability Power (x3) - Standard quintessences for every AP mid
• Greater Mark of Magic Penetration (x9) - Also standard for every AP mid
• Greater Seal of Scaling Health (x9) - Katarina is a little squishy early on so you need the health to win trades. From level 6, the scaling health seals help better than the flat health seals, and since you shouldn't go all-in before level 6 unless you are 100% sure you win, you should pick the scaling ones.
• Greater Glyph of Magic Resist (x4) + Greater Glyph of Scaling Magic Resist (x5) - You don't build much magic resist with this build apart from a Guardian Angel (and maybe an Abyssal Mask). We use a mix of flat and scaling magic resist because you will be taking magic damage in lane (flat helps better there), and the scaling ones help you better in the mid / late game. You can also go with 9 times flat or 9 times scaling, it's all a matter of preference.

Offensive tree
Double-Edged Sword - Your goal as Katarina is to deal damage, so dealing 2% more damage while taking 1% more damage is a good trade.

Sorcery - I take two points in this because Katarina benefits more from the cooldown reduction than she does from the attack speed.

Butcher - Two more damage against minions makes for easier last-hitting, but you can skip this one for another point in Sorcery.

Expose Weakness - You will be damaging your enemies with your spells a lot, so there is no reason to not take this.

Mental Force - Katarina is an AP carry and therefore needs ability power.

Arcane Mastery - See the above explanation ^

Executioner - If you all-in a champ and suppose that half of the time he is above 50% health of his and half of the time under 50%, this boosts your damage with 0,5 x 5% = 2,5%.

Archmage - You build get around 500 ability power with this build (30% from Rabadon's Deathcap not counted, so this increases your ability power by 25. It's like Arcane Mastery, but four times better.

Dangerous Game - You will be killing a lot of people so this could help you a lot. And then I haven't even mentioned the fights you win in lane with just 10 HP left.

Devastating Strikes - 6% magic penetration is actually quite nice, because if you do well your enemies will get magic resist and now it will look like they have a little less.

Arcane Blade - For every 20 ability power your basic attacks deal one more damage. Not too useful, but "the best of the rest".

Havoc - 300 damage Bouncing Blades + 250 damage sinister steel + 250 damage

Shunpo + 2000 damage Death Lotus makes for about 3000 damage. An increase of 90 (3%) could make the difference between getting a kill or not.

Defensive tree
Block - You are a melee so will get smacked some basic attacks in your face from time to time. The reduction of two will start to add up after a few hits.

Recovery - Having a little more health regeneration is always nice.

Unyielding - Just like Block , the reduction starts to add up after a few hits. If you get hit ten times, you already have 40 health more than you would have had without these two masteries.

Veteran Scars - 36 more health can be the difference between surviving or not a surviving a level 6 all-in.

Juggernaut - I find an increase of around 60 health to be more useful than two armor or magic resist. Oppression isn't even worth mentioning.

Starting items
You will want to start with Boots + 4 Health Potions in 99% of the cases so you can get your Sorcerer's Shoes faster. You can also go for Cloth Armor + 5 Health Potions if you are against an AD heavy opponent. You get a Stealth Ward to make up for not getting any Stealth Wards and to use your Shunpo on for escaping ganks.

First back
You should always rush Sorcerer's Shoes, because the magic penetration helps you deal more damage in lane and the movement speed helps you roam faster. You can go for Mobility Boots if you roam a lot, but you will lose magic penetration which you don't get in this guide apart from a little bit from your runes and masteries. If you have farmed enough in lane and picked up a kill or two, you can also pick up a Needlessly Large Rod to boost your damage a lot. If you don't have enough money, you can also get a Fiendish Codex or Seeker's Armguard. Pick the former if you're rushing a Deathfire Grasp, pick the latter if you're rushing a Zhonya's Hourglass. Always get a few Health Potions and Stealth Wards as well.

Mid game
By now you should have roamed a few times and farmed even more. You turn your Needlessly Large Rod (or Fiendish Codex / Seeker's Armguard) into a Deathfire Grasp or Zhonya's Hourglass. I get a Deathfire Grasp first if I feel like I'm not getting focused and I need the little extra damage to one-shot the enemy mid (because you can easily do that with Deathfire Grasp + all your spells!). I go for a Zhonya's Hourglass if I get focused a lot and need the extra survivability.

Late game
The next item you get is a Guardian Angel. If you don't engage at wrong moments and know what you're doing, you should never die if you have this and a Zhonya's Hourglass. Imagine an unkillable Katarina who deals sick amounts of damage.. pretty scary huh? To boost your damage even more you get a Rabadon's Deathcap. With the 120 extra ability power and 30% bonus you should have around 500 ability power by now. Finish it off with a Void Staff to counter their magic resist. Somewhere in the late game you should also upgrade your Greater Totem into a Greater Stealth Totem

Optional items
Rylai's Crystal Scepter works good on Kat too. It gives you a nice chunk of health and a slow on all your abilities which makes kiting easier. The reason I don't see this as a core item on Katarina whereas others do, is that you are already pretty hard to kill and the slow shouldn't be necessary if your team follows you up in fights.
Abyssal Mask is actually a pretty good item on Katarina. It makes you tankier, and helps you deal more damage in two ways (through it's passive and of course the ability power it gives). But again, you won't die very fast. I'd only take this item if my enemy had no magic resist at all or I had another AP carry on my team. If you take this item, replace it for the Void Staff.

Items you absolutely shouldn't get
Hextech Gunblade. A mistake I often see is Katarinas rushing a Hextech Gunblade. It costs way too much for the stats it gives. Let's do the maths behind this. I will put down the stats it gives with the money it is worth in brackets.
65 ability power [1413,75]
20% spell vamp [550]
45 attack damage [1620]
12% life steal [528]
Active [800 money (just an estimation, there are no exact numbers known for this)]
Total cost: 3400 gold [4911,75]
"Huh, Pallis123, it's actually worth way more than it gives!" you might say. But you don't use the attack damage apart from 135 more damage for one Death Lotus, which is negligible. The life steal you don't use at all. If you don't count this stats, the item is worth 2763,75. You just wasted 636,25 money, well done. If you feel like you really want spell vamp, go for a Will of the Ancients. The ability power and spell vamp it gives are worth 1637,5 gold, with 10% cooldown reduction on top of that, netting a total of around 2000 gold which is exactly what the item is worth.

Voracity - Passive
This is an awesome passive. If you get a kill or assist, your three basic abilities are immediately off cooldown and after three kills or assists your ultimate will also be up again. If you turret dive your opponent in lane and manage to kill him, you can quickly use shunpo again to jump to a target minion so you take one turret hit less and maybe survive where you would otherwise have died.
In teamfights you can use your abilities more often, resulting in picking up easy kills on running targets.



Bouncing Blades - Q
You usually pick this skill first and max it second. You can use this to last-hit minions from afar and harrass your opponent without coming in range to take damage yourself. You can also max this first if you're really getting zoned, but the only thing that gets better if you level this is the damage, the cooldown doesn't go down. Meaning that if you use it to take one or two last-hits, you will still have to wait eight seconds before you can use it again and you will probably have missed a lot of creeps by then. (You get it? Don't get zoned! :P)

sinister steel - W
I take my first point in this skill at lvl 3 and max it from there on. It has a four second cooldown, so it gives you an easy way to last-hit minions as well as sustained damage in trades. If you are against a melee champion you just press w everytime they try to last-hit a minion and then run away with the speed buff, it's as easy as that.

Shunpo - E
Shunpo is a blink that can be used defensively and offensively. Gank incoming? Jump away to one of the minions and wait until the jungler has gone away. Enemy low health and you want to kill him? Jump on him and unload your combo.
Tip: Always keep a ward with you so you can put it down and jump on if there aren't allies / enemies / minions close. You max this skill last as you mainly use it for utility.

Death Lotus - R
One of the most potential ults, and this separates the good Katarinas from the bad ones. It deals a ****load of damage but is interrupted easily. You should wait until the enemy has blown their crowd control before you use it. You should use it everytime it's up and your enemy has used their crowd control, because it has a low cooldown.
Tip: Wait in one of the side bushes for your enemy to roam and then use your ult, because it won't reveal you!

Generally spoken: Death Lotus > sinister steel > Bouncing Blades > Shunpo

Laning phase
Bouncing Blades + Shunpo + sinister steel
This one is pretty self-explanatory. Throw your Bouncing Blades at your enemy, Shunpo in their face and use sinister steel. After that run away with your speed buff and try to evade incoming skill shots.

Shunpo + Bouncing Blades + sinister steel
Most Katarinas don't jump on their enemy without using Bouncing Blades, so they won't expect you to do this and maybe not run away whereas they would immediately do that if you had first thrown a Bouncing Blades to them.

Bouncing Blades + sinister steel
Just use this everytime a melee enemy tries to last-hit a minion close to you. He has to choose: either take 100 damage and get a last-hit, or don't take 100 damage but miss the last-hit.

And, the combo at level 6 which should kill your enemy:
Bouncing Blades + Shunpo + sinister steel + Ignite
Use the first combo described, but instead of running away start ulting and Ignite your enemy. This won't interrupt your ult. If you get off a full Death Lotus you should deal 1000 damage and kill your enemy. Just don't get interrupted or die before you kill him.

Mid / late game (teamfights)
Deathfire Grasp + Bouncing Blades + Shunpo + Death Lotus + Ignite
Use the Deathfire Grasp active on a squishy carry, throw Bouncing Blades on their whole team, Shunpo in on the same person you used your Deathfire Grasp on and start Death Lotus. Ignite doesn't matter too much at this stage of the game, unless you can put it on some health regeneration beast like Dr. Mundo. The 200 damage from sinister steel isn't worth the precious time you could use your Death Lotus, so skip it.
If your team follows you up and you got off your full Death Lotus, you should know be able to start jumping from target to target with the resets you get from Voracity.

Buy your starting items, head over to mid lane and wait until the minions come. You shouldn't help with leashing your jungler, unless he gets really mad. Throw a Bouncing Blades in then.
In lane you should do what every other champion does: farm, farm, farm and don't take too much damage while doing so. In the first few levels just last-hit minions with your basic attacks. If one is out of your range, throw your Bouncing Blades on it. Try to not do this too often, because you will push the lane and be prone to ganks. If the enemy starts to use his spells or pushes te lane, however, push back! Losing your turret is something you also don't want to happen.
Once you get two or three points in sinister steel, you should never miss a last-hit. Auto-attack the low ones, use sinister steel if there are two low at the same time and throw your Bouncing Blades if they are out of your range. Two out or your range ready to get last-hit? No problem, Shunpo in and use sinister steel.
Try to make the other mid laner scared of you by using the above described combo's. Your sinister steel has a very low cooldown so don't be shy with using it every single trade. If he is at about 50% of his health, you can all-in kill him at level 6.
Keep your sidebushes (or at least one of them) warded, so you see incoming ganks and they don't appear behind you out of nowhere. If you have warded one side bush, stay a little more to that side. You know you're safer and if they choose to take that way, you can jump to the ward.
If at level 6 you can't kill your enemy midlaner, try to hard-push the lane to his turret and go gank another lane. If no lanes are overextended, just keep farming, farming and farming.

By now you should have your boots and either a Deathfire Grasp or a Zhonya's Hourglass. The first turrets in lane will have fallen and teamfights occur now. If you get off some good Death Lotuses, you should be able to clear the teamfights up with the resets. But keep in mind, you also need the farm! Don't run around for five minutes for only one teamfight, because you miss a minion wave or seven, eight then.
Mid game is all about getting objectives. Turrets, dragon, baron nashor, they all grant global money and are therefore worth more than getting one or two kills.
Make sure you have enough Stealth Wards around dragon and a Vision Ward inside the pit. Dragon is worth around 2 ~ 3 kills, so if you lose one member in the teamfight but manage to get dragon it's still a good deal. You can also try to sneak it, but only if you have a Vision Ward around. Same for baron nashor, but this is a lot harder to pull off.

You should reach (or already have reached) your final build by now. One of the teams or both of them is close to taking the nexus and the game has almost come to an end. If you win one teamfight in this stage of the game, it's usually a win. People are dead for 60 seconds and the way to the nexus and its turrets should already be open.
If you are losing, try to always keep one member of your team defend the nexus, while one splitpushes and the others keep the enemy team stuck in any lane they try to come through. Of course this won't always work, but it's well worth the try.

You have two roles in teamfights: the first one is to jump in on a squishy carry and get off as much of your Death Lotus as possible, the second is to finish off low health opponents with your resets.
To achieve the first one, you must wait for the enemy to use their cc. Not just a few, all. Only a stun or a silence already is enough to interrupt it, and you can better wait a few seconds and get off a full Death Lotus!
Once enemies are out of your range and one of them gets killed, you can chase the running targets with your Bouncing Blades + Shunpo + sinister steel combo. Repeat this a few times, and if everything's gone right you have won the teamfight by now.

• Always get two or three Stealth Wards when you back. Ward your sidebushes, or even go a little deeper in the river and in your enemy jungle! The last ones are often luxury, but they warn you for an incoming gank a few seconds earlier than the wards in the sidebushes would have done, so they give you some precious more time to run away. Also, if you spot an enemy jungler passing by on low health you can go in and kill him. Some champions, like Katarina and Lee Sin can also use the wards as escape tools.
  
• Know your enemy's cooldowns! Champions are vulnerable when they have just used their full set of spells, so you have a little window to harrass them without taking damage back. If you repeat this over and over, the chances are you will win your lane.
  
• Try to push your lane, but only if you have your bushes warded. Taking the midlane turret or just giving yourself some time to gank another lane is very important as a midlaner. And on top of that, if the enemy just backed he will lose xp when you push te minions to his turret.
  
• Ward your enemy blue buff and try to steal it at around 7:05.

This was my guide, I hope you enjoyed it! Leave a comment to tell me what you thought of it and don't be scared to give criticism (however I prefer it to be constructive)