First at all - I'm not a diamond pro player or something like that. I play in S2 but I'm not even active in ranked games. I prefer normal games to test stuff like AP- Aatrox without ruining my ELO(which is already ruined^.^).
In this guide I'll show you how I play Aatrox, known for AS-heavy AD as a convincing AP-Midlaner.
Don't flame me for bad english or a bad structured guide, it's my 1st one.
The basic idea about Aaptrox is: A with 100% AP scaling ultimate and up to 110% bonus attack speed with max. filled Blood Well + max. skilled Massacre must me useful when using the reworked Nashor's Tooth.
I tried it and well, it worked out:
As you can see, as planned, I tried to buy a Nashor's Tooth in early game.
This game, I had to play against Swain, which was really frustrating because, as I found out later, playing against point&click Champions like Swain, Ryze or Katarina is the most annoying thing in early games with Aatrox because you are just not able to take CS.
Here
are some
other Screenshots
More about Aaptrox you will be able to read in the following chapters.

I always prefer Flash and Ignite.
Instead of Flash you can also play with Ghost.
Depending on your gameplay you should choose for yourself. The reason for me to play with Flash is the extended Leap-Range( Flash-> Dark Flight).
Ignite is something like a insured kill.
Instead of Ignite you can play with Barrier(if you tend to towerdives) or Teleport to perform prearranged ganks on top or bot.

The runes are definitely the part of the guide about which I am most uncertain.

Greater Mark of Magic Penetration
I prefer Marks with Magic Penetration to make the first skilled Blades of Torment more powerful for pokes and quick wave-clears.
Greater Seal of Armor
Season 3 revolutionized the AD-midlane. With Zed, Kha'Zix, Pantheon, and many others the chance to play against AD-midlaners is really high. For that case I play with armor in seals. 9* Greater Seal of Armor provides ~12,5 Armor from level 1. In addition to his base armor of 17,8 he has exactly 30,5 armor at level 1.
Greater Glyph of Magic Resist
The runetype, which provides the best magic resist is also used for it. 9* Greater Glyph of Magic Resist=12,06 additional magic resist. With these runes Aatrox has a level 1 magic resist of 32,3, which reduces the magic damage, dealt by opponents casters, definitely noticeable.
Greater Quintessence of Ability Power
The use of AP-Quints improves the damage of Blades of Torment and, logically, the damage of Massacre by ~15.

To be honest, I hate masteries. I really don't know what to say about such an easy decision.
I play 21/9/0, that's all I have to say 'bout my Aaptrox masteries.

I'll try to explain every single decision of Items as detailed as possible.

Boots

The boots themselves depend on the opponent.
The Enchantment of your Shoes depends on your gameplay and is highly dependent on the situation. 95% of all players within my elo-level(including me) just go for Homeguard Shoes to be faster on lane.

Fiendish Codex

The Fiendish Codex is an AP-granting item which also has a 10% cdr boost.
The fact that on early lanes Blades of Torment is the only really possibility to poke the opponent AND that the Fiendish Codex is needed for Nashor's Tooth, makes it the perfect item to buy next to some wards and pots when you go back the first time.

Nashor's Tooth

As explained before, I thought about an early Nashor's Tooth.
(I try to be as correct as possible) with ~500 AP the Nashor's Tooth deals 90(15+15% of AP) as additional damage per hit. With an attack speed of ~1,80( an easy crackable value with Nashor's Tooth and max. filled Blood Well + max. skilled Massacre) you deal ~160 bonus damage with autohits per second.

Rabadons Deathcap

Rabadon's Deathcap is a recommended item for almost every single caster in League of Legends. You can buy it to increase your damage for a huge amount or don't buy it to have a slot for another item which provides more defensive power.

Liandry's Torment

This is definitely one of my favorite "new" items in LoL. It provides everything you need: Health, damage and a great passive. I like it to pick up a Haunting Guise within the first 15 minutes of the game and finishing Liandry's Torment pretty late.

Will of the Ancients

To make it easy for me to explain and easy for you to understand:
Aatrox' abilities cost health - WotA grants health for damage.
With this item the self inflicted damage is just instantly healed.

Lich Bane

Like other ap champions with a single dmg spell on lane like ap Gangplank and Master Yi, Aaptrox just has his E to deal damage without using Massacre.
Lich Bane is a great possibility to increase your damage early and especially much. After using Dark Flight or Blades of Torment, try to get in autohit-range and inflict the Lich Bane bonus damage.

I start with my E( Blades of Torment) to be able to pull the junglers start camp AND/OR to poke the opponents midlaner already at level 1.
The 2nd skillpoint goes to my W( Blood Thirst) to have some sustain on the lane.
To be able to operate with the allied jungler I give the 3rd skillpoint to the Q( Dark Flight).
After skilling Blood Thirst a second time at level 4, I concentrate at maxing the E first. Followed by the Q and finally by the W.
As usual Massacre gets skilled at 6/11/16.

PROS:

+high range poke
+"easy" level 6 towerdives(even without jungler)
+high range gapcloser
+with Zhonya's Hourglass, Aatrox is unbeatable for ~6seconds
+it's really really funny to play
+high sustain


CONS:

-the damage until you reached level 6 is below the midlane average
-it's quite hard to play because Aatrox is really squishy
-it's almost impossible to start a teamfight without Blood Well up

From Level 1-5, you should just try to "outfarm".
Sure, thats not always possible, but when it's not, try not to get outfarmed.
You can permanently poke with Blades of Torment but even for early engages Dark Flight costs too much health to be profitable.
Playing against other melee's will be easier than playing against early nuke-champs such as LeBlanc or Lux.
At minute 15, a farm of 80-120 should be your goal. When you have less than 80cs after 15 minutes, and you don't got downcamped, you should probably just try to learn correct farming before:-) . Especially when your passive is currently up, you should try to play as aggressive as possible. I'll upload some Videos soon.
Be happy whenever you are able to cast Massacre and just dealing up to 1.000 AoE-damage.

Try to farm as much as possible.(Numbers:^)
When you were able to poke/nuke your opponent out of the lane, you can use Dark Flight and Blades of Torment to quickpush the wave and taking the own/opponents wraith/wolf-camp.
As I told before, Aaptrox needs level 6 to burst down other mids. When you weren't able to kill the opponents midlaner up to now, you should have farmed a Fiendish Codex and some Wards to make an secured kill.

Aatrox is a legendary warrior, one of only five that remain of an ancient race known as the Darkin. He wields his massive blade with grace and poise, slicing through legions in a style that is hypnotic to behold. With each foe felled, Aatrox's seemingly living blade drinks in their blood, empowering him and fueling his brutal, elegant campaign of slaughter.

The earliest tale of Aatrox is as old as recorded history. It tells of a war between two great factions remembered only as the Protectorate and the Magelords. Over time, the Magelords won a series of crushing victories, leaving them on the brink of obliterating their sworn enemy forever. On the day of their final confrontation, the Protectorate army found themselves outnumbered, exhausted, and poorly equipped. They braced for inevitable defeat.

Just when all hope seemed lost, Aatrox appeared among the ranks of the Protectorate. With but a few words, he urged the soldiers to fight to the last before throwing himself into battle. His presence inspired the desperate warriors. At first, they could only watch in awe as this unknown hero cleaved through their enemies, his body and blade moving in unison as if one being. Soon, the warriors found themselves imbued with a potent thirst for battle. They followed Aatrox into the fray, each fighting with the furious strength of ten until they had won a most unlikely victory.

Aatrox vanished after that battle, but the Protectorate army's newfound fury did not. Their surprising triumph led to many more until they were able to finally return home victorious. Their countrymen hailed them as heroes, but though they had saved their entire civilization from destruction, darkness lingered in the mind of each warrior. Something within them had changed. Over time, their memories of battle faded, only to be replaced with a grim revelation: their acts of heroism were, in fact, brutal atrocities committed by their own hands.

Tales like these appear among the myths of many cultures. If they are all to be believed, Aatrox's presence has changed the course of some of the most important wars in history. Though these stories remember him as a savior in dark times, Aatrox's true legacy may be a world filled with conflict and strife.

"Some fight for honor, some fight for glory. It matters only that you fight."
-Aatrox