Welcome to my Corki Guide , please enjoy and don´t be so hard . And get a look on my other builds too :)

Pros


+ High single target burst damage
+ AOE damage
+ Shreds armor
+ physical, magical and true damage
+ Excellent farmer
+ strong poke and harass
+ strong early-mid game nuker
+ Amazing late game dps
+ built in flash-like ability
+ Urfrider skin is epic



Cons


- Mana dependent without Manamune
- auto attack range is 550
- Lacks any form of CC.
- Low base movement speed
- Somewhat hard to play and master

21/9/0 for higher damage output, and some survivability.
I actually thought that when Riot will nerf Flash( btw I'm actually very happy they did), I'll go full utility to have my flash with lower CD. But once I saw the new offensive tree, I knew it is too awesome to miss. Note that the new mastery trees have much less strict set-ups than the old trees, and they allow players to be much more creative and unique when it comes to choosing masteries. So feel free to try new things and play around with different set-ups and masteries, and find yourself the set-up that suits your playstyle.


Offense


Weapon Expertise and Sunder are mandatory.

Deadliness and Lethality Will incrase your late game auto-attack damage.

Executioner and Havoc in combination with Hextech Shrapnel Shells is insane.


Defense


Hardiness and Resistance: Will improve your durability a bit. The bonus armor is very useful in the laning phase.

Durability and veteran's scar more health, which means more survivability. Can't go wrong with this.


*I find that 9 points in the defensive tree is better than 9 in the utility tree, however 21-0-9 is also viable.

** For build 3 I Invest more than 21 in the offense tree, because I want to get 3 points in Vampirism, because in build 3 I get the bloodtherstier very late in the game, so I need extra life steal. After I get the 3 points in life steal, I can't get veteran's scar, so I just put the rest of my points ןמ improved Flash, some armor, and further more in offense. You can choose to take 21-9-0 for build 3 as well and just get an early Vampiric Scepter.

Best choices

Flash
By far my favorite spell. Great for squishes who need a fast get the **** out button. Combined with your Valkyrie, you are very hard to catch.
Ignite: Decent spell for Corki. Securing early game kills, nice true damage late game to finish off tanky enemies.
Viable choices

Exhaust would be my next choice after Cleanse, if the enemy team has very little CC. It is a great spell, for duelings, chasing, escaping, and stopping anti-carries like Akali, Irelia and Nocturne from killing you in team fights.
Ghost: a possible spell for more mobility.
Teleport: Possible , with it you can port to pushed lanes and destroy towers, and farm huge minions waves. However there are more important spells for you as a carry to take.
Heal: Very strong spell after the buff. Very nice spell to have on your team, if someone on your team already took Exhaust, consider taking it.

hextech shrapnel shells An excellent passive for an AD carry. Note that is also scales with Sheen and Trinity force procs.


Phosphorus Bomb
A strong harassing tool in the lane and your only utility. This should be maxed for high magical damage output very early on, and allows you to be a threat even before you got any of your core items.
Instead of the partial blind this skill used to have, it now detects enemies for 6 seconds. I know that many people are disappointed with this buff, but I have to say that I think Riot did really good job. The partial blind was pretty op and made it impossible for almost any AD champion to 1v1 him. Giving him that ability back would have made him OP again. However the detection make this ability useful again, without making it OP. Corki obviously still needs a few tweaks, but Riot are definitely going in the right direction.


ValkyrieYour escape/reposition/chase ability, And an amazing one. Huge range, and with a decent cooldown. In team fights, its almost always better to use it defensively rather than offensively. While escaping, use it to jump over walls. If you bought Manamune, spam it in order to move faster around the map.
Max this last, for obvious reason. It is an escape mechanism, and 1 point in it is enough.



Gatling Gun This is your melt face ability. Just spray the enemy team, shredding their armor to nothing. A very cool thing about this skill is that it keeps firing even if you are stunned.
I max this second. Like all AD carries, your auto attacks will be pretty weak early game, and so this skill isn't vey strong at early levels. I prefer to focus on being a nuker early game, by maxing Phosphorus Bomb. Gatling Gun, In contrast to Phosphorus Bomb, it is pretty weak early, however it becomes stronger and stronger as the game progresses.
*The remade to Gatling gun didn't really change Corki. It does a bit more damage per second now, since 68 is higher than 40% of Corki's base AD. Basically the remade made the skill strong at early levels, But made it weaker at max rank, due to the fact that the old Gatling lasted for 5 seconds at rank 5. This remade didn't buff or nerf Corki, and according to Riot, it was just made so they will be able to buff Corki in the future without accidentally turning him OP like he used to be. could


Missile Barrage Amazing skill which is used for poking, harassing and increasing your DPS.
AOE, and super long range. Once you get this, you should be able to dominate your lane.
Use it in lane to harrase. Poke with it before fights. Spam it in the start of the fight to deal massive AOE damage. Scout bushes for campers. And of course, shot it between autoattacks to greatly increase your damage output. Before a gank, make sure you have the Big One ready. At lvl 7, Q+R combo kills the 3 mage minions.
Its possible to steal baron/dragon with it. If you have vision on the Baron/Drgaon and the enemy team are doing it, click on the monster to see it's health, charge a Big missile, and wait for the right moment to shot. It's extremely hard to beat smite with it, but doable