Most people say that you can not jungle Katarina. But I thought if you gank and u get one kill your passive is just destroying all other championsremaining in the lane. I tried a lot of things especially because of the sustainability. Your ganks with Katarina are amazing.

This are the runes working well for me. You could change the Quintessences to get more armor for even more sustainability but the sustainability is good enough in my mind. The ability power makes your ganks more powerful, especially your ultimate.

The creeps in the jungle will not make it easy for you in the early-game, this is why u need as much masteries as you can get to reduce the creepdamage. The rest of the masteries I set to help you stay alive in the jungle and make you more powerful.

Get your Cloth Armor first and take five Health Pots, you will need them!
If you finished your first jungle and maybe a few ganks u will buy Boots of Speed and you will aim for Sorcerer's Shoes.
Get a Blasting Wand and a Negatron Cloak and make a Abyssal Scepter to get MORE magic penetration.
->Your early-game-damage is not depending on your AP, it depends on your MAGIC PENETRATION!
Go on and get a Giant's Belt, a Blasting Wand, an Amplifying Tone and make them to Rylai's Crystal Scepter.
Now you are a little bit OP. Get a Guardian Angel to annoy your opponents even more.
The next step is to increase your damage rapidly. This means you need a Rabadon's Deathcap!
And even if it got nerfed so hard I prefer to get an Deathfire Grasp to nuke the first enemy down -> Don't remember, ur passive is OP.

Start with your W for the highest damage-output over time. It will help you to kill the Bluebuff pretty easy with a normal onehit-leash. You don't need a hard leash on the bluebuff. I will telll you why I start blue in the jungle-chapter.
Go on with skilling your Q as second skill.
After that you need to get your E to gank.
Max out your Q for the highest damage output in a single burst.
After maxing Q, max W. and E as the last skill.

I guess it's obvious why I chose Flash and Smite.
Nothing more to say.

Star at the bluebuff, you need the cooldown-recudtion to spam your W in the jungle.
Finish Wolves and Wraiths and kill the Redbuff to get your Level 3.
You don't need to necassarily kill the golems.
Now look for some ganks.

Hide in the bush until you get the range for your Q, if it's out you will go E>W for the highest burstdamage you can deal. Since you reach level 6 your single damageoutput is enough to kill a single target.

->Ganking Botlane
This is a special situation becuase you have two opponents to kill.
Tell your AD Carry and your Supporter to kill the target with the lower health first, even if it is the supporter.
You will deal damage to the AD Carry seperately and if you have your Cooldowns resetted it's an easy second kill.

It's important to not engage.
You need the perfect timing and positioning to be not bursted down by all opponents immidiately. Make your passive work by killing the targets, you can one-burst, first.
YOU NEED SMARTCAST TO BE MOST EFFECTIVE!
Just go Q>E>W or only E>W and make your team able to win the match in a few seconds.

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This is my first guide. Feel free to comment, rate, whatever. I think I'm too lazy to insert lots of pictures making it more comfortable to read it.
Try it out guys. This works.