Hey, my first build i created here, the only reason i decided to do a build guide is that when i was playing first time katarina, i owned during mid. The only reasons when i didnt own is when it was a 3v5 or my team was all support. Hope you like it! It has something new than the other guides!

First of all, you want to get some ability power for an early game advantage. Getting 9 AP glyphs will be enough as they are double than the seals and marks. Magic Penetration Marks which will allow your abilites to do more damage to someone with magic resists. And of course magic resist, the defense against mids, which only happens to be AP users having talon and a few others as exepctions due to the ability to silence a ap caster. And just plain ol' flat sp quins which gives you 15 AP extra. These runes will give you an advantage in early games as that will allow you to poke/harrass often without being poked/harrassed back and do much damage. You can get a kill at lvl 2 when you got shunpo. Ill explain later.

Adds little benifits but all for a better early game. 21/9/0 should be the number for Katarina.
21 in offense which; 4 in Mental force for Ap, 4 in sorcery for Cooldown reduction which means Katarina can spam abilitys which cooldown is shorter, 1 in arcane knowledge for Magic Penetration, 3 in Wreak havoc for a 1.5% more damage, 4 in blast for AP per level. 4 in archmage which increases your total AP by 5%(kinda like a mini Rabbadons Deathcap) and 1 in Executioner for more damage below 35% health.
8 in Defense which; 3 in flat Magic resist, 1 in Flat armor, 4 in durability for health per level, 1 in veterans scars for extra health.

The whole point of the defense skills is because Katarina is very squishy when it comes unfair 1v1 or 2v1 fights. She isnt much early game when she doest have the health/ap needed to kill the other target. The health from defense can help her out while farming and who doesnt want extra health?

This one has a different approach. Early game, get bouncing blades as it is your mains source of damage but also, since you are not a ranged carry, bouncing blades will help you a lot by casting it on a minion, it can bounce to an enemy. Stay behind the minions as most ap carriers have skill shots which can ruin your laning. Keep spaming bouncing blades until lvl 2. Get shunpo and if the target is low health and a bit further away the turret. Lure him or play passive to think you arnt going to attack him and he might forget you have shunpo. Then use shunpo on him and bouncing blades. Ignite and shunpo back. The combo for katarina's goes as this: Q-E-W-R which Bouncing Blades>Shunpo>sinister Steel>Death locus. She can own in a 3v5 fight if you get your positioning right. shunpo in the middle of the battle and death locus can take down all 5 opponents without a single death from your team.

If you are having a hard time in mid or you are not getting kills(1v1 evenly) or you think mid is too easy, why not gank? With katarina, its easy with shunpo and ulti to gank but to execute the order, you need to be clever. When you finish a minion wave, go into the brushes on the side and make your way to perform the gank. The mid enemy champ will think you went back to base or backed off and waiting for minions to continue, which in short term, he/she will not ss or mid mia. You can then gank without the 'gankees' knowledge of you.

Just my first guide so please tell me what you think. I didnt add the rest of the guide as i never did jungling/ranked yet so i cant judge that. I did however win 6 times and lost 2 times with my first time kata mid. Please be positive. Thx!