This is my first guide and I wrote this guide simply because I love this champion and have more fun playing him than any other and to allow newer Kayn players to have a more comfortable time getting to know his strengths and weaknesses as this is a strong set-up that enhances Kayn's Rhaast kit to the fullest.

This build has helped me personally improve my gameplay with him substantially especially with the introduction of Stormrazor (replaced Phantom Dancer in my build) which allows for you to boost your damage with a guaranteed crit and bursts of movement speed in between your spells as you should always link your spell casts with AA's(I'll talk more about this in the Items section).

As far as the build order of the item's goes, i usually try to get my Enchantment: Warrior asap followed by Ninja Tabi / Mercury Treads & Black Cleaver, after which sometimes i rush into Death's Dance sometimes I get a little beefier with Spirit Visage or get saucy with an early Stormrazor.

For the Runes I chose the Domination & Precision trees due to the added AD & AS helps early game jungle clears and your late game sustained pressure.

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The Domination Tree

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Electrocute is my keystone of choice but Dark Harvest works as well, simple playstyle choice.

Sudden Impact is an absolute must on Kayn in my opinion, it activates everytime you use Reaping Slash and provide a much needed Lethality boost to couple with your %HP damage on Reaping Slash & Umbral Trespass.

Eyeball Collection is just better than the other options in the tree as they're mostly utility you won't need;
Ghost Poro won't work well since you're always changing bushes so it won't stay in one place & Zombie Ward could be useful if you need to keep tabs on a particularly invasive opposing jungler.. *cough* Ivern *cough* , so extra damage is always nice.

Ravenous Hunter Self-explanatory.. extra Healing.. which you already do.. a lot.

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The Precision Tree

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Triumph is an amazing jungler rune as assists also count as takedowns thus giving you a little extra, extra gold when you show you team some love. On top of the small gold boost it gives, during teamfights for each takedown you're a part of you'll regen a large portion of %Missing-HP which helps you stick around longer, pair that with Spirit Visage and you've got some nasty regenerative abilites.

Last Stand is my personal choice as you're going to be in plenty of drawn out fights which lead to HP rising and falling so boosting your damage when you're low will give you a bit of a spike to rocket your healing capabilities and win that nasty heal off against Darius or Warwick; Legend: Tenacity is another strong pick if the enemy team has plenty of CC.

My build is pretty standard when you look at other possible builds so why would I post it you might ask? Well that's simple, there's subtle differences... wait did i just say DIFFERENCES in League Of Legends!!?? .. yes, differences that make my build unique and can help score the upperhand; the basics like Enchantment: Warrior, Black Cleaver, Spirit Visage are all great, you'll always see them on Kayn because they help make him tick.

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Things I usually see on other Kayn's when y'know... people steal him from me Q.Q are Dead Man's Plate, Maw of Malmortius, Warmog's Armor, Sterak's Gage, Youmuu's Ghostblade. While These are all nice items to finish off your build they have their problems;

Dead Man's Plate; Gap closing item, jungler travel item, armor & health. Requires time to build up the speed for the proc effect and could be replaced by Thornmail as well as an item I will mention soon~

Maw of Malmortius; Magic resist, AD, CDR, effectively an old Surge on low hp for Spell Vamp + Lifesteal. The activation of the Surge only triggers when you're low on hp which most times will leave you dead anyways to more burst heavy teams.

Warmog's Armor; Raw HP, Raw HP Regen, Some CDR, there's just better options.

Sterak's Gage; HP, Base AD increase, triggered shield effect.
Although the triggered shield effect can save you the changes made to the item require a more substantial bonus HP pool to make it worth it.

Youmuu's Ghostblade; AD, CDR, Lethality, Active movement speed increase, Rhaast doesn't need it.

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My choices to replace these items with better options happen to be Death's Dance & the new Stormrazor(I used to use Phantom Dancer but i like this more).

Let's start with Death's Dance; AD, CDR, a passive that let's you still damage you take into DoTs, Healing equal to a % of your physical damage dealt. The passive allows you a bit more time to regain all that health you just lost to a Alpha Strike or Pyroclasm coupled with the %Healing you can get it back with ease if you can survive the onslaught, not to mention Kayn is completely physical in Rhaast form unlike his passive in Shadow Assassin form so every single hit you land heals you stacking from Rhaast's passive, Ravenous Hunter, Spirit Visage and now Death's Dance making for a whole lot of healing your opponents weren't ready for.

Now for the new toy, Stormrazor; 70 AD, 30% AS & a unique passive Storm's Edge.
This item caught my eye the moment I saw the art and name so I was intrigued, on reading that it was a crit item that was based on stuttering your auto's to repeatedly gain 100% chance to crit was new to me, then I thought about how I was enjoying the more fluid chain playstyle of Kayn and I thought if i were to auto between every ability cast(which you should be doing regardless!!) then Storm's Edge would proc every time I were to AA an enemy thus allowing for an even heavier sustained output from Kayn's fast & fluid chain's and this has indeed proven to be the case, the movement speed let's you catch back up after landing your quick touch and go Reaping Slash -> AA cheese or you can knock them up with Blade's Reach then add in a saucy AA to let you run along side them before throwing in another AA or Reaping Slash -> AA. Needless to say this item has been pleasing to use and I do recommend it.