Hullo this is my way of playing Evelynn, the AP way. She can be used in the jungle, or as a good laner, but this particular build is bad at early game, and a total beast late game. I will get further into what to do in lane early game and how to pick up easy kills late game.

IGNITE - Very helpful for killing runners and good for bursting down faster, all around a great choice.

GHOST - Very good for chasing while stealthed, since you should be taking sorcerer boots, even with lichbane you might not be as fast as you want to be.

EXHAUST - Great for 1v1ing and taking down runners.

FLASH - Amazing escape tool or trick while stealthed, but since you already have stealth to get away fast, there is no extreme need for this spell.

Take a point in Q first, this will help you farm creeps early at the start. Take 2 points into W after, 20 seconds of stealth is all you should need to perform a good kill. At 4 take Ravage, use it to open on an enemy. After you have all 3, max Q as you will need it to farm in lane. You won't have enough AP early game to make Ravage do a lot of damage, so it is not worth it yet. After you max Q, making sure to take your ulty every level it's available, max Ravage. Again, you only need 20 seconds in stealth really, after that it's all about the stun. Then obviously max Stealth.

R > Q > E > W

Magic Pen. Runes and Quintessences are important in this build, combined with Void Staff and Sorcerer boots Eve will be able to destroy any champion out there. For Yellow I take Health just to help early game, as I said before, this build isn't good till late game. For Blue I take ability power to help early game and late game, as you are heavily based off of ability power.

For masteries I take a simple Offense build, not taking anything in Crit as you probably won't ever get one. Make sure to go into improved Ignite, That SS can be insanely useful even though eve is a great turret diver. I usually take Utility for the mana regeneration; you will be spamming Q a lot so you need some way to regain after that. I also put a point into ghost, it is great for moving fast to chase while stealthed.

First I like to pick up a doran's ring for the ability power and the regen, you can take a Amplifying Tome if want to build Mejai's faster. Next I take sorcerers, the magic pen is essential. If you didn't build Mejai's first, take it now, it is your first source of AP, Eve doesn't die much so you shouldn't lose stacks, however it is slow gaining them early game. After that Rylai's is the way to go, it is very useful as they will be slowed every second while you spam Q. After Rylai's work you way to Rabadon's, you will start to be able to slaughter any champion in a matter of seconds, after that finish strong with Void Staff to destroy anyone you please.

EARLY GAME - You mainly want to lay low with stealth or in the grass as you will die pretty fast and you can't kill very fast yet. If there is no one around make sure to farm the creeps fast with Q. When there are MIA's just use stealth and look around in the nearby jungle to see if it's you they're after.

MID GAME - You will have a little bit of AP at this point and your ultimate. Now you can start picking off easy kills. If they are champions like Xin or Panth that are cheap easy game, don't go for it. If they have around have health and don't turret hug they are a perfect target. If they have ~200 HP and they are near a turret, go for it, you are healed after the kill and can easily escape into grass.

LATE GAME - After you get all your AP and Spell Pen you can do about 1000 damage with you Ravage, and then 700 with your lichbane. Don't engage a target unless your ulty is up, it will help A LOT. Make sure to open with E as it will further reduce their resistances. Then just spam Q and chase.... Make sure that your team members go in before you, they may see with an oracles and kill you within seconds.

Thank you for reading my build, I hope you enjoy playing Evelynn this way, make sure to come back and rate or comment after you try it.