Kat is a very high damaging champion who has mobility with her Shunpo and her Bouncing Blades can be used to bounce up a minion wave and then to kill a champ. One of her most interesting aspects that is necessary to take advantage of is that she has no mana! Also her passive refreshes some seconds off her cooldown when she gets a kill or assist. She can be countered by good stuns and taunts which stop her in her tracks and also cancel her Death Lotus. Fighting against tanky fighters makes it harder for her to harass and dealing a good amount of damage.
In this guide, I will show you how to dominate your mid with ease.

Starting with marks, i prefer magic penetration to get through the early game magic resist (if they even have any) and to do maximum damage. Other possibilities can be ability power or cooldown reduction (not the best choice for marks). Attack damage marks are a viable option because in mid, there are mostly ap champions who probably have magic resist to counter other mids.
For seals, i get flat ability power again, for more damage. Magic resist can be used here but armour is less preferable due to the lack of ad champions who go mid. Cooldown reduction is another good choice to spam those spells.
Looking at the options of glyphs, cooldown per level is nice to have so one, there is some cd reduction in her rune page and two, she can use her spells more often which mean more damage. Some armour or magic resist is decent but cooldown reduction or ap of some kind is better than that.
Quints of Potency is my quint of choice for more of that extra damage. the usual ap, cd reduction or magic penetration is a good choice. Other runes are a no go because the quints have a larger effect on your champion.

My mastery page is pretty straight forward but there are some masteries that are necessary. Sorcery, Havoc and Executioner are really good to have to stack cd reduction, and to increase all kind of damage.
In the defensive tree, i lean towards Resistance instead of Hardiness for those ap mids. The rest in the defensive tree is just to go with your play style.
The utility tree is not good with Kat because the defence tree at least gives her more survivability.

Starting with a Regrowth Pendant and pot might seem unusual but in lane, the extra health regen is extremely useful and gives a lot of sustain. it also helps that Kat doesn't need mana so a mana pot is out of the question and so are every item that influences mana. That lets us just get straight up ap.
Next up is the Hextech Revolver. The ap and spell vamp is good enough for now and you still need boots.
Sorcerer's Shoes is pretty straight forward. If you want other boots then Ionian Boots of Lucidity and Mercury Treads are pretty good choices.
Rylai's Crystal Scepter is an amazing item for the fact that it gives Kat way more survivability, alot of ap and the slow on spell is important. Having your enemy in your ult for one second longer can mean a kill that never ran away.
Rabadon's Deathcap is the last core item and this item gives a whole lot of ap. When it is calculated just the Deathcap alone is 182 ap! that's good ap from just one item. The passive of this item is that it increases your ap by 30% of it. This is a necessity to have in your build.
So by late game people will probably get magic resist so you can counter them by getting Abyssal Scepter. The extra ap is useful but on this item the aura is the good part. Pretty much every enemy in your area has their magic resist decreased by 20. This item can be switched with some ap items like Void Staff or Zhonya's Hourglass (activating this during Kat's ult cancels it).
The rest of the build is just finishing off what you started. If you often to forget to use actives go with Will of the Ancients, if not then stick with Hextech Gunblade. You can replace regrowth pendant with Guardian Angel or Banshee's Veil.

Bouncing Blades:
Katarina throws a dagger that bounces from enemy to enemy, dealing magic damage.
This is useful for farming and harassing. Use it whenever you can to farm/harass. The trick to the bounce is that it only hits a target once. So while a minion wave is lined up and on its way, throw it up the wave and if the enemy champion is near the wave, they should get hit.

Killer Instincts:
Passive: Katarina's attacks deal increased damage. Active: Katarina's next basic attack has a bonus effect. Bouncing Blade deals full damage to every target hit and reduces incoming healing to the target, or after using Shunpo Katarina takes reduced damage for 3 seconds.
Having one point in this until level 14 is fine because no matter what level it is, it always grants full damage on Bouncing Blades. Use this and Bouncing Blades to reduce the effect of your enemy's health pot. It can be used to reduce damage when used with Shunpo and that is useful for when you ult in 5 people.

Shunpo:
Katarina instantly moves to her target's location. If the target is an enemy, she deals damage.
This is an amazing spell, it can be used to initiate a fight (make sure the fight are a definite kill when alone) or to get away. Shunpo lets you teleport to wards, all champions and all minions but not towers. This is the reason you should not hesitate to have one extra ward in your inventory to telepot to (you can place and Shunpo to the ward over walls). That trick is pretty much another flash, just make sure to use that getaway combo quickly or have the ward already placed.

Death Lotus:
Katarina goes into a state of extreme focus, throwing daggers with unrivaled speed at up to three nearby champions.
Yes, this does say only 3 champs will be hit by it but with the cooldown reduction that i have been talking about, you can use it almost 3 times a team fight (mostly 2). Do not try Zhonya's hourglass with her ult because it is a channelling spell and any movement or item actives will cancel it. You can however use summoner spells like exhaust or ignite while it is active.

This section will be relatively short. Basically the point is to max out bouncing blades to increase the number of bounces. Early game this can be used to bounce a lined up minion wave and hit your enemy to harass while getting farm. Next to max out is Shunpo, with all this ap shunpo does nice initiating damage. I mostly use Killer Instincts just for Bouncing Blades which makes each blade do the max damage on each bounce. Level up her ult whenever you can, plain and simple.

The spell choice is fairly simple, flash is an instant Shunpo without a taget. Ghost is less preferable because you won't need the continuous speed, you need quick, instant movements. It should be used when there is nobody to Shunpo to.
The second spell can be either ignite or exhaust. You can use both spells while using Death Lotus and has their advantages. Ignite is useful for that extra unavoidable damage and exhaust is good to slow the enemy in the ult.
Cleanse is... okay. I'd rather get Quicksilver Sash but only if there is so much cc, when I Shunpo in I am immobilized and dead instantly. I normally don't get any of these.

Pros:
- Very mobile
- Incredibly low cooldown (you can even spam ult)
- High damage while hitting multiple tagets
- Possible to snowball hard with her (did bravery and won)
- Good against mid champs
- Shunpo to almost anything

Cons:
- Squishier than the average champion
- Weak against stuns, suppress etc.
- No necessary role in the team comp
- No cc
- Mana-less champions (Mordekaiser) or champions that can spam spells make mid more challenging

Fist you wanna buy your items as fast as you can and head to the brush behind blue to leash with a Bouncing Blade ever the wall. If you're invading then just go with the flow and follow your teammates.
In lane it would be best to use the range on Bouncing Blades to get some last hits on minions until Bouncing Blades can bounce some more. The point of it is to get farm and harass with one blade. At this time Shunpo is more of a utility spell however i sometimes use it to get cs. Just be sure not to be in range of damage just for one cs. When Shunpo is on cooldown and you're pushed further than the river line, be careful for ganks. If you followed my runes and masteries, you shoud be able to ult whenever you want. For example Oriana just came back from recalling and your spells are up. Use killer instincts and bouncing blades, then Shunpo and use Death Loutus (ignite if you want the kill) so that after the combo, Oriana needs to recall again. By the time she comes back, your ult should be off cooldown.
Do not hesitate to get wards because one, you're vulnerable to ganks from both sides of the lane and two, you can teleport to them in the brush and make them think you have an ally hiding there.
If you're extremely pushed hard or have the mid tower gone, go ahead to get fed off the other lanes, don't expect a guaranteed kill for the fact that Kat has no cc (rely on allies to stun the target).
A good counter to stealthed ganks is her ult. Normally, when there isn't anyone in range, the picture of the ult will be gray. When someone is nearby, the picture will be coloured which means it can be activated. That also means when a stealthed champion comes in range and Death Lotus isn't on cooldown, the pic will be coloured.

Here you should get most of your core items or at least Rylai's. The slow helps get way more kills. All i can really say here is stay with your team and participate in team fights, just do not initiate or chase too far (prob bait). If nothing is happening then push your lane by default or help with another lane that needs help.

At this time there should be one team near the other's base. Stay and cooperate with your team and if they go in a team fight that is a sure loss just Shunpo away. Try your best to determine whether or not your team could have won with you. The death timers here are very long so by all means do not die, if everyone else on your team is dead and the enemy is taking a tower, unless they are at 100hp each do not take them on. Do not go for a bouncing blade toss because they WILL dive you if you're solo and stun you and the death timer will be annoyingly long.

So Kat is my favourite champion to play and i played her since i started and bought her as soon as I could have (she was free that week). She is a very high damage champion that can dominate mid. Her spell spamming is the reason for that.
I hope that you will be able to make use of this guide and do well. Maybe you might even play me as Kat mid.

-Pictures. I know that i need them and i will be working on it.
-Improvement of the general look of the overall guide