Why hello there, welcome to my Katarina guide!
Katarina is a very underrated champion, in my opinion. Everyone seems to think that she sucks, without having tried her before. Well, you can change everyone's view on Katarina, with this guide!
Katarina is a strong AP carry, with a high skill cap, but once you learn how to use her, you'll become an unstoppable killing machine!

Pros

Can snowball really easy and very hard.
Tons of AoE damage.
High mobility, with Shunpo.
Can reduce healing done, using Preparation combined with Bouncing Blades.

Cons

Gets countered hard by CC.
High skill cap.
Can be countered easily.
Melee auto attacks, making last hitting in mid lane much more difficult.

For summoners I pick Ignite and Flash.

Flash is always a great summoner, especially if you make a mistake, and don't have your Shunpo ready to make up for it.
Instead of Ignite you can choose Ghost for more mobility, but I usually just get Ignite for the extra damage in the laning phase.

For runes I get:

• Magic Pen marks, to increase Katarina's damage output from her abilities.
• Armor seals, to be able to stay in lane longer, since you'll most definitely get harassed a bit when against ranged champions in mid.
• Magic Resist glyphs, for more tankiness in the mid lane.
• Flat AP quints, for more damage in the laning phase, since you can just spam your Bouncing Blades everytime it's on cooldown.

I choose to put 21 points into the offense masteries, to maximize the damage that I'll be doing. The last 9 points I put into Defense to be a bit tankier, since the utility masteries aren't really that great on Katarina, since she's not mana based.

Passive: Voracity
This passive is just awesome, and it's amazing for teamfights. It's why Katarina is able to snowball very hard, since she gets bonus gold for kills/assists.
But the best part is the cooldown reduction each time she gets a kill/assist. In a teamfight, you'll be able to use ult twice, if you get a couple of kills, which can lead to some pretty epic multikills.



Q: Bouncing Blades
This is a very great poke ability, probably one of the best. It's also very good for teamfights, since it'll bounce to everyone near your target. Combined with the heal reduction when using Preparation you can counter healers.
When laning, you can use this ability on a minion to make it bounce to the enemy champion, if he's trying to go in for a last hit.
Tip: When your lane match-up pops a health pot, try to put the heal reduction debuff on him, so he won't gain as much health from the potion as he normally would.



W: Preparation
A pretty good skill with different uses. It passively increases the damage done with all of your abilities, which is really great since Katarina has a lot of AoE damage. It can either be used to make you tankier, when you combine it with Shunpo, or apply healing reduction to your enemies, if you combine it with Bouncing Blades.




E: Shunpo
Great spell, and makes Katarina fun to play. This ability can be used to jump to enemies, allies, wards and creeps, so there's opportunity to make some pretty awesome plays and jukes using this spell.
Remember that this spell will teleport you behind your target, so it can also be used to dodge skill shots.
Tip: Always keep a ward on you, in case your Flash is down and you need to escape. Simply just put down a ward, then Shunpo to the ward, and voila; you're gone. :)



R: Death Lotus
To quote the great Phreak: "Tons of damage". You'll be doing insane amounts of damage with this ability, but beware that it'll require a bit of practice before you know when and where to use it and how to use it properly.
Tip: You can hide in a brush and use this ability when your enemies come close to you, much like Nunu's Absolute Zero, without the enemies not even getting time to react before they're pretty much already dead.

Always max Bouncing Blades first, since it's great for laning, farming and harassing. Max Shunpo second, as this ability is part of your main damage output.
Remember to max Death Lotus whenever you can, and max Preparation last, getting one point in it at level 4.

Core build

I usually start out with Boots and 3x Health Potion to have more sustain in lane, and for the extra movement speed, to dodge enemy skillshots, etc.
If you don't want to start boots and 3 pots, you can also start either Doran's Shield for extra tankiness, or Amplifying Tome and 1x Health Potion for extra damage, although I recommend boots and 3 pots.
The first item you should buy is Hextech Revolver, since it will give you a lot of sustain, when you spam your Bouncing Bladess in lane.
After the Hextech Revolver you should finish your boots into Sorcerer's Shoes. The extra magic pen will increase your damage by a bit.
Tip: When I go mid I usually pick up a sight ward or two every time I go back, for a more secure lane.

Full build

Now, after you've got your core build, there are several items that you can choose to build.

• Hextech Gunblade
  This item is just amazing for Katarina, since her ult scales with both AP and AD, and the active slow is also perfect combined with your ult. It's like this item was made for Katarina. I usually start out with buying this as my first main item after my core build, but it's just my personal preference.
  
• Rylai's Crystal Scepter
  Another great item for Katarina. The +500 health will make you a lot tankier, plus you'll get a slow when using your spells, plus some ability power. I buy this right after Hextech Gunblade, but I'll buy it before Gunblade if I'm feeling like I'm too squishy. You'll both deal damage and be tankier with this item.
  
• Rabadon's Deathcap
  What's there to say. Tons of damage. You'll do literally tons of damage with this item. I usually first get this item after Rylai's and Hextech, but if you're doing well you can rush Deathcap and hurt like hell.
  
• Zhonya's Hourglass
  This is more of a situational item. If you feel like you're not getting much done in teamfights, being focused down way too quickly, you should buy this. When I have Zhonya's, I usually use my E into the fight, then pop my Hourglass to put off the enemy team's timing, and then pop ult. This tactic will give you a bit more time to be helpful in teamfights.
  
• Mejai's Soulstealer
  This item is also very situational, and I rarely get it. I only get this item if I know that I'm going to get a lot of kills, and that I won't die. So, choose wisely, it can either be a great succes or a disaster.
  
  Max spell vamp trick: You can get up to 52 % spell vamp if you buy a Hextech Gunblade, a Will of the Ancients and then a Hextech Revolver. This way, you get all the unique passives by having 3 spell vamp items. You should only do this if you want to have a "troll" game, since it's not really that effective, and my normal build will be much better on Katarina, this is just a fun little trick. ;)

As stated previously, Katarina is easily countered, mostly by CC. Since this is the case, she naturally has a lot of counters, but I'll just post a couple of her worst laning matchups, and of course the champions she dominates in lane.

Try to avoid these champions when playing Katarina:

Sion is a very good counter to Katarina, because of his natural tankiness, his shield and his stun. If you're against a Sion with Katarina, you're probably not going to snowball, since he'll just push your lane, leaving you at tower trying to last hit.


LeBlanc is another great counter to Katarina, since she can silence you and probably one-shot you if you try to go in on her. Ouch.


Another low cooldown silence. Kassadin can either silence you when you ult, or just ult out himself. It can be very difficult to get close to this guy.


So. Much. CC. Not much else to say, but Alistar is a very good pick against Katarina.


Same thing as Alistar, but even worse. Silence, CC and a grab. Damn.


Janna has a lot of CC as well, and she can even push you out of team fights. No fair! :(

Katarina is very good against these champions:

Poor Karthus. No stun, no silence. He can't do a thing if you go in on him, except Flash away from you.


Lux has many skill shots. Katarina is very good at dodging skill shots. Do the math ;).

Check out my website for full games where I play Katarina, and some cool little videos, including a 1v3 triple kill ;)

Katarina is an underestimated champion, and she's very fun to play, plus she has the ability to potentially carry games.

Thanks for reading my guide, don't forget to give me feedback!
Now go out there and pwn some n00bs with your newly aquired Katarina skills :D