Hello Guys, my name is HDfeeling and im a EUW Kayn main and i just wanted to share my build with you. It may not be optimal but that is what i use and somehow i got it to Mastery 7 within 40k Masterypoints.

My native language is german so dont wonder if something here is spelled wrong :P.

As Kayn you can choose once in the game with your passive The Darkin Scythe if you want to be an assassin or bruiser. If you attack ranged champions you will get blue orbs which fill your passive "circle". By attacking melee Champions you get red orbs when your circle is filled you are able to choose between Shadow Assassin or Rhaast

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As Shadow Assassin you deal crazy amounts of damage with your full Combo.

As Darkin / Rhaast you heal with almost all of your abilitys and have nice cc with your w.

Electrocute is optimal as Shadow Assassin for you. This rune provides nice damage for you. Even as Rhaast its a very good Rune.

Sudden Impact synergizes in general very good with your kit.

Eyeball Collection is just for more damage.

Relentless Hunter is very good because of that out of combat movementspeed which is very nice as Assassin.

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Secondary Rune Path depends on which Form you are going.

Shadow Assassin

Reaping Slash (Q): Its your primary Spell in the jungle for farming. First Kayn performs a dash and then rotates in a circle around him. You can also dash through walls with your Q.

Blade´s Reach (W): Your W does the most damage. As Shadow Assassin you leave a shadow version of yourself behind you which allows you to cast your w while moving.

Shadow Step (E): Allows you to move through terrain once entered you get healed and 70% bonus movementspeed. Your E also removes slows.

Umbral Trespass (R): Your Ult gets extra 200 range.

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Rhaast

Reaping Slash (Q): Its your primary Spell in the jungle for farming. First Kayn performs a dash and then rotates in a circle around him. You can also dash through walls with your Q.

Blade´s Reach (W): Your W does the most damage. As Rhaast your W knocks enemies for 1 second up .

Shadow Step (E): Shadow Step doesnt get changed in Rhaast form. Your E also removes slows.

Umbral Trespass (R): Your ult heals you for 7% (+ 9% per 100 bonus AD) of target's maximum health.

Auto attack

Your W Blade's Reach: Shadow Assassin will be cast the second you Q Reaping Slash: Shadow Assassin which does a absurd amount of damage. The Auto Attack is important because it will prock your Electrocute and does a lot of damage. If your target survives you can Ult to finish it off.
If you are enough ahead you probably can kill a squishy champ without even using an auto attack.

I found it usefull to mention that it is more easy to clear raptors and wolves if you Auto them first then W Blade's Reach and then Q Reaping Slash. Your Auto Attack lets them chase you which makes it easier to hit your W