Hello, I'm Stopkilling0 and this is my first guide. I enjoy playing Dominion, and even more so, playing AP (Ability Power) Evelynn in Dominion. I have seen a few Dominion guides that build a hybrid / AD Eve. But I really wanted to make a guide that focused solely around AP Evelynn.
I believe that AP Eve is far superior to AD/Hybrid builds and I will attempt to explain why in this guide.

For runes I use movement speed quints, flat AP glyphs, flat mana regen seals and flat magic pen marks.
I use flat runes instead on scaling runes because I think winning that first fight at top can really help you snowball throughout the rest of the game.
-The movement speed quints provide a speed advantage over people not using these runes. This is important because later in the game, you will want to be able to burst someone sitting at a point and slip away, then come back and finish them off. I find that the extra movement speed really helps in this aspect.
-The AP glyphs are there to help your initial burst when going for top, and throughout the next few levels.
-I use mana regen seals because early in the you can really get mana starved, even with all the health packs (which you done want to waste time running around for in the beginning anyways) and your mana potion, I find that by have this little extra bit I can squeeze out a few more spells at the end of the day. Can be life-saving
-I use magic pen marks because you want to be prepared for people getting paranoid of you early on and building merc treads or other magic resist items. This way, if someone buys an anti-magic mantle early, I can still take them on.

I almost always take 21/0/9
Putting points into everything that will increase your AP is essential because remember we're going for a strong early game presence, and frankly without these masteries you won't really have one.
Take movement speed in utility for the extra boost to poking power and death timer reduction.
Chances are that you are going to die in Dominion because of its faster pace, and I cant tell you the number of times I have saved a point because of points in this mastery.

I start with a blasting wand, boots, and pots.
Now you might be asking "No prospectors ring!? But the vale is incredible with +200 health, AP and mana regen!". And you are correct, it is an amazing vale and still a great buy if you prefer to go that route, and you can even still buy boots with money to spare this way.
I start with blasting wand not only because it provides me with more AP, but because it also builds in Lich Bane, which is your most important (core) item. The faster you can build this item the faster you are going you start snowballing.
Boots are in my mind, self explaining, ability to chase, run away, and poke more than anyone else thanks to our movement speed runes and masteries.
Potions are only 35 gold a pop now, even mana potions (used to be 40). Don't be stingy and save that last little bit of money at the beginning of the game. You are a sneaky character who is going to be poking people and going to back stealth quite a bit. Might as well regen a substantial amount of health and mana while you're doing it.
After this I start building Lich Bane, and mobility boots
I usually go for sheen first, but the great thing about building lich bane is that you can build up to it for a variety of situations. Go sheen first if you are doing fine, and have not died to high AP squishes yet. Go mantle first if you get dominated by them. You can build your boots whenever you feel like it, some games I build it before I finish LB and sometimes after. If you feel like you're having to B a lot, the boots will help with getting back into position near top or bottom lane.
Then build your Deathcap
Once this is finished, and even once you get your large rod, you will really start to see your damage output soar, with your AP going to around 245 after you build your cap.
With your high atk speed from your ulti, LB damage that abuses hate spikes, and 1:1 AP ratio ravage, you really start to become a serious threat.

At this point the game should be coming to a close and you can start building situational items.
Personally I like to build nashor's tooth, building stinger first.
I find that the extra attack speed, ability power and cooldown reduction really compliment the needs of end-game fighitng. The stats from this item focus on boosting your damage output from LB and hate spike attacks. Hit more often with attack speed, and hit even more often with CDR for hate spikes.

Take 2 points in ravage, and 1 in shadow walk at the gate.
Try to convince your team that you are going to be capping mid, you have great burst and you really benefit your team by coming a little later in the fight at top and really dominating the enemy champs that now already have low health and can be easily bursted down.
If you capped mid, you're going to reach Lv.4 before you reach top so put a point into hate spikes.
If you didn't cap mid, then the 2 points that you have in ravage will help get some early damage out of the gate to help win top.
After that the skill order is
Malice and Spite >>> Ravage >>> Hate Spike >>> Shadow Walk
Take another point in shadow walk at level 7 for extra duration because I feel that at that point in the game 10 seconds just is not enough time to get into a good position undetected.
Ulti first for obvious reasons.
Ravage second because its your main source of bursty damage.
Hate spikes next for even more damage.
Shadow walk last because who needs to be in stealth for more than 20 seconds anyways?

Ignite and Ghost are my two favorite summoner spells for Dominion mode.
Ignite will help the fight at top quite a bit, and still provide a healing reducer mid/late game for those pesky champion who have heals (Alistar im looking at you), with the 20% healing reduction from the crystal scar aura, and the 50% from ignite, it becomes almost obsolete allowing you to quickly finish off an opponent.
Ghost is great for Dominion because it allows you to get around faster at key moments in a mode that has a large focus on mobility, not to mention you are Evelynn! You already build large amounts of movement speed, and using Ghost, combined with your ulti and a speed shrine, you can essentially get anywhere on the map in no time flat, saving that all important point or running off to turn a 1v1 into a 2v1 very fast.

You can also take flash and maybe surge, but that's up to you, I've had the most success with these spells.

Pros:
-High burst takes out almost any squishy glass cannon carry in no time flat
-Stealth allows for surprise burst, its like when you wait the the bush on any other champion
waiting to spring your trap, except your bush is everywhere! (lawl)
-High mobility allows for the ninja-ing of points and poking power
-LB + Hate spike provide good sustained damage even after initial burst
-PPBO all over the place, let them waste their money, Dominion is still filled with actual bushes to hide in

Cons:
-Squishy, but not that big of a problem because of high mobility and slow from SW
-Has trouble killing Tanky DPS 1v1, never 1v1 a Darius/Jax or the like unless they are very low on health
-If this is your first time playing Eve, you may not want to build AP, if you cannot snowball because you don't have the right experience with champs like her, chances are you're going to fall off in damage.
-People think Eve is bad because of SR (Pro?)

I will be updating this guide a lot more sometimes soon, adding BB code, detailed play style guide, and the like. But the NA servers just came back up, I'm off to play Eve.


Constructive criticism is greatly appreciated as this is my first guide
Thank you for reading!