Firstly, welcome to my guide :D. I'm making this guide because, Katarina Katarina is one of the most fun champs to play,in my opinion of course. I haven't played Kat hundreds of times like other guide makers do..but I found a very effective way to play Kat very actually who can contribute with both damage AND crowd control. BTW....this guide was made with my experience as someone who plays Kat mid, unless I'm solo top 1v1/2v1.

Pros:
-Tons of damage
-Very slippery when chasing
-Very hard to gank with flash/shunpo
-Easy to harass with
-NO MANA!!

Cons:
-Squishy early game
-Hard to farm with against far ranged champs
-Her ultimate, Death Lotus , gets disrupted by almost EVERY CC.

For Runes, I go M.Pen marks, HP/Level Seals, CDR/Level Glyphs, and M.Pen Quints. All for damage and easier farming.

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I also find CDR/Level Quints viable, too.

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For masteries I go 9/9/10. I got 9 in offense for the extra damage, 9 in defense for the extra armor/MR/and health for when I jump into team fights, and 10 in Utility for movement and a little spell vamp.

Ok..so this is the main highlight of my build. I'm pretty sure most of the above is pretty standard. The exception probably being going 21/0/9 in masteries, or Magic/Armor Pen. for runes. Most Katarina players I see usually go for the max damage output by going Sorcerer's Shoes, Hextech Gunblade or Will of Ancients, Rylai's Crystal Scepter, Rabadons, possible Meijai's Soulstealer, and Voidstaff/Abyssal Scepter.
In my build, I go for a semi-tanky build. Firstly, I start off with and 3 for the reason of farming/harassing before the enemy can do any damage on you. With this easy way of farming, I then save up enough for my . With the spellvamp from this item, you can farm and harass forever if you in your lane because Kat doesn't use ANY MANA!!!! Now with your , I just keep it until needed. I usually save it for my last item, for you won't really be upclose melee fighting for the lifesteal anyways.
For my third item, , I make it my #1 priority after my revolver. The reason I rush if afterwards is that slow works amazingly with her abilities, mainly her . Kat herself has no CC. Adding a slow to all of her abilities would already make her a CC packed champ. Now, for what I think is the MOST important item for her. . This item...is soooo amazing for Kat. When I play Kat, I love to initiate with my Shunpo>Deathlotus. The bad thing is, you will be focused first. But with Zhonya's, you can just negate all the damage that will be focused towards your for a couple of seconds. The thing about this is, mages will waste their skillshots on your, maybe some ults will go off pointlessly, and AD carries will walk around aimlessly not knowing where to go, all while your team is making their way to the already weakened team. You could let your team initate, and you Shunpo in so that your Death Lotus will not get disrupted by any cc that the have.
The next item, , is also an amazing item for her. It provides you with many options, both benefiting to yourself and your team. One example, is when chasing an enemy, you can just Shunpo to them and activate it to slow them down. This can also work for running away, activating it, and then Shunpo to a friendly unit. For benefiting to your team, Shunpo into a large teamfight and activate it to decrease the ad carries attack speed.
The next item is , which is an obvious reason..MORE AP = MORE DAMAGE!!
Finally, I finished up my , using the active to slow down enemies when running away/chasing. And also, I just finish up my Sorcerer's Shoes whenever I feel necessary.

For early game when playing 1v1, use your Bouncing Blade Bouncing Blades to farm as much as possible. Activate it with your Killer Instincts Preparation whenever you want to harass your adversary from far away. Just note that it won't always target your enemy. When you want serious damage against your enemy, use W>E>Q>R, ( Preparation > Shunpo > Bouncing Blades> Death Lotus ). With this combo, you want to be persistent with your Death lotus Death Lotus, because early game your enemy can't really outdamage you during your ult, because that is 10 knives going their way. Just be wary of any CC besides slow and Lux Lux, Ryze Ryze, Morgana Morgana suppresses.

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W>E>Q>R

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Preparation > Shunpo > Bouncing Blades > Death Lotus

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A tip for finishing off any champion under many circumstances such as:
-Champions guarded by other enemy champions
-Champions under tower
...Use the shunpo Shunpo in and out technique. With your passive, everytime you get a kill or assist, your cooldowns refresh by 15 seconds. That is enough for all your abilities except your ultimate to go off cooldown. With this, you can just shunpo Shunpo for the kill, and shunpo right back out onto an ally or any minion/ward. You can also repeatedly shunpo Shunpo on enemies for kills over and over.

My main tip is: DO NOT BE AFAID TO USE YOUR ULT..THE COOL DOWN IS SUUUUUUPER LOW.

Farming............................................................
..Words cannot describe how incredibly important farming is..Farming can be much better than any champion kill. A normal champion kill for Kat is around 255-325 Gold, considering her passive. That is tantamount to around 20 or so minions. Just use your Q repeatedly on minions for the farm. My motto for farming against a stronger champion is "If you can't out - harass, the out - farm them."

This concludes my guide to a Tanky/CC packed Katarina. I hope this changes your experience with her, as it certainly has for me. Thanks :]~