Hi i am sman9998. Although i am not a high rank i feel my guide is very complete and will help out aspiring Aatrox players. I play about 3/4 of my ranked games as Aatrox, both top and jungle. I have raised myself from bronze 3 to silver 5 so far using him. Thanks for reading my guide.

Aatrox, the Darkin Blade is a melee fighter champion whose versatile abilities specialize in strong initiation and self-sustain. Possessing exceptional attack speed and durability from his passive, Aatrox excels as a duelist and initiator, leaping onto single opponents or entire teams, recovering from injury just by trading blows, applying pressure from afar, and can even briefly empower himself to aggressively pursue fleeing foes. (http://leagueoflegends.wikia.com/wiki/Aatrox)

Aatrox is a very strong laner, and played the right way, can dominate a lane, no matter who the other team throws at you.

Pros-
Turret buster
A LOT of sustain
A pretty good amount of cc
LOTS of AOE damage
Very good split pushing and wave clearing
Very Good at defending
Easy start in jungle and very fast camp clearing
Did i mention turret buster?

Cons-
Hard CC can destroy you
Damage over time effects can hurt as well
Q and E require a lot of accuracy to land
Hard to learn how to W toggle effectively

Flash- Flash is a very good summoner spell, allowing for you to teleport a small distance, such as a through a wall or structure. This is essential for when you get stuck in a bad situation and your jump is on cooldown.

Teleport- After a few seconds you teleport to allied minion, ward or tower. This can mean the difference in who wins a lane. With teleport you can back and go back to lane very quickly without giving up any hits on your turret. Later in the game, teleport can be used as a tool for splitpushing, if the wave is in the enemy base, or to get back from split pushing if your team enters a fight or wants to take an objective. It can also be used if your team is in the middle of a fight without you to get quickly into the fight and help turn the tide. Aatrox teleports can be especially brutal because you can teleport, qre combo and nuke the enemy team.

Ignite- Although ignite is a useful spell, i generally rely on my teammates to bring ignite. Ignite an be used to secure kills or to stop health regen. With Aatrox you could use it against laners such as mundo or volibear to cancel out a lot of their healing.

Top-
Ravenous Hydra- This item i feel is the most essential part of Aatrox. It allows you to hit everyone near you, and in conjunction with the attack speed of your ultimate, you can hit the whole enemy team at once for moderate to excellent damage.

Spirit Visage- The passive effect of 20% bonus healing can allow you to stay in lane longer, stay in fights longer, and to take objectives such as baron and dragon without losing too much health.

Blade of the Ruined King- The lifesteal, attack speed and damage is pretty good and allows for more sustain and faster nuking. The active effects can stop people from escaping fights and to initiate fights or nuke the adc

Maw of Malmortius- Reading the item says it all. More damage you take, more damage you deal. More damage you deal, more regen. Its a cylcle and Maw is an essential part.

Zephr- More AD, always good. More attack speed, even better, more CD reduction, more combos. The main thing is the tenacity. This will allow for you to be more in the fight, less cced.

Bloodthirster- A LOT of AD, and 10% lifesteal. This can make getting back to full easy. Run into the jungle, kill a camp, boom full health. The shield can take a good amount of damage during the initiation of a fight, or save you from death during a fight.

Guardian Angel- who doesnt love 3 lives? If you are carrying your game hard, get this. It will have you keep coming back, and in conjunction with lifesteal you can get back to full health easily everytime you come back up.

Thornmail- Pretty self explanatory. If they have a lot of AD, get this so they kill themselves.

Warmog's Armor- A ton of health, a lot of health regen. Useful in between fights if you don't want to back.

Randuin's Omen- A lot of armor, useful against AD teams. The slowing effect is good for securing kills if your q is on cool down.

Jungle-
Stalkers blade- I prefer this item over the other jungling items because you are going for hard initiations and kill secures with Aatrox jungle. Dive over the enemy team, ult, smite and BoRK the enemy carry and the fight will be yours.

Devourer- gives you a nice bonus for clearing camps, to make up for a lack of AD in the build.

Passive- Blood Well-
Whenever Aatrox uses an ability that costs health, he stores 100% of the health cost into his Blood Well. The maximum amount of health the Blood Well can store is equal to 30 + (45 x level). If Aatrox has not dealt or received damage in the last 5 seconds, his Blood Well will deplete at a rate of 2% per second.
Upon taking fatal damage, Blood Well activates and places Aatrox in stasis for 3 seconds. Over the stasis duration the Blood Well is emptied and Aatrox restores health equal to its contents plus 10.5 + (15.75 x level). Blood Well's activation has a static cooldown and is unaffected by cooldown reduction.
Also, Aatrox passively increases his attack speed by 1% for every 2% in the Blood Well(30/35/40/45/50/55% upgrades every 3 champion levels)
Cooldown: 225/200/175/150 (at levels 1/6/11/16)

Aatrox's passive is a revive. You can use it to dive someone, to tank a turret and get back up and to turn the tide of a team fight. You can run in do your full combo, and if you die, come back and do more, possible winning the fight or surviving so that you can take an objective or defend. Now that there is a lower CD as you level, you will have a lot more opportunities to fight without risking death.

Q- Dark Flight
Aatrox takes flight and slams down at a targeted location, dealing physical damage in a large area. Enemies in the center of the blast are also knocked up for 1 second.
Range: 650
Cooldown: 16 / 15 / 14 / 13 / 12
Cost: 10% of current health
Physical Damage: 70 / 115 / 160 / 205 / 250 (+ 60% bonus AD)

This is your initiation. Using this you can knock up any number of champions that you get in the center of the landing zone, setting up a play for the rest of your team or securing a kill in lane. Keep in mind that any cc taken during flight will carry over, such as morgana snares or garen silences. Flip abilities, such as volibear or singed's flip will stop you from flying. Having your passive and dieing mid flight will result in suspension in the air, after which you will drop down right below the point of suspension.

W- Blood Thirst
Toggle Off: Aatrox heals himself on every third attack. If Aatrox is below 50% health he will heal for three times as much.
Cooldown: .5 seconds
Heal: 20 / 25 / 30 / 35 / 40 (+25% bonus AD)
Enhanced Heal: 60 / 75 / 90 / 105 / 120 (+75% bonus AD)

This can be used to heal in the lane, so that you dont have to back, and to farm the jungle without taking too much damage.

W- Blood Price-
Toggle On(Blood Price): Aatrox deals bonus physical damage on every third attack at the cost of health.
Cooldown: .5 Seconds
Bonus Physical Damage: 60 / 95 / 130 / 165 / 200 (+100% bonus AD)
Health Cost On Third Attack: 15 / 23.75 / 32.5 / 41.25 / 50 (+25% bonus AD)

This is your W's toggle. It can be used to turn a fight if you need that bonus damage, or to poke an enemy who is trying to farm in lane. Be careful though, as it does cost health and if you are using your ultimate in conjunction, you can drop health really quickly.

E- Blades of Torment-
Aatrox unleashes and sends forward the power of his blade, dealing magic damage to enemies in a line and slowing them by 40% for a few seconds.
Range: 1000
Cooldown: 12 / 11 / 10 / 9 / 8
Cost: 5% of current health
Magic Damage: 75 / 110 / 145 / 180 / 215 (+ 60% AP) (+ 60% bonus AD)
Slow Duration: 1.75 / 2 / 2.25 / 2.5 / 2.75 seconds

This is your primary zoning cc for lane. This skill shot is tough though. As it travels, it gets narrower, making it harder to hit someone the farther it has to go, although the benefits of hitting both sides of the skill shot are nice. If you hit someone with the tip of the skill shot, they take damage from both blades. A good tip is to send it where they will be not where they are.

R- Massacre-
Aatrox draws in the blood of his foes, dealing magic damage to nearby enemy champions. Massacre grants 20% of Maximum Blood Well for each enemy hit
For the next 12 seconds, Aatrox's gains bonus attack speed and 175 bonus attack range (325 total range). He is still considered melee for item purposes.
Cooldown: 100 / 85 / 70
Cost: No cost
Magic Damage: 200 / 300 / 400 (+ 100% AP)
Attack Speed: 40 / 50 / 60%

This ultimate is exactly what its called. A massacre. Used in combination with a Q initiate and a followup with a E slow, you will do TONS OF DAMAGE. When you pop your ultimate, it will do AOE damage to all nearby enemies, be it Baron, Superminions or that pesky Teemo. After the AOE you gain a ton of attack speed, and turn into a "ranged" champion. If you have a Hydra, enemies will melt like butter, but what do we care about? TURRETS! You can drop a turret from 100 to 0 in no time at all with your ult. It will explode. Since it turns into a 70 second (without CDR) cool down at level 3, this makes Aatrox one of the best, if not the best, split pusher in the game.

OFFENSE: 21
Double Edged Sword- Lets you hit Harder, even though you might take a bit more damage. (1pt)
Fury- Increase your attack speed significantly. (4pts)
Butcher- Makes it easier to farm early on. (1pt)
Brute Force- equivilent to AD per level runes. (3pts)
Feast- Gives you more sustain in lane and rewards more for last hitting. (1pt)
Martial Mastery- More AD. (1pt)
Executioner- Gives you an edge while dueling in lane, and makes your e pokes do more. (3pts)
Warlord- More AD. (3pts)
Devestating Strikes- Your e pokes will do even more damage, as it is a hybrid move. (3pts)
Havoc- Increases damage overall. (1pt)

DEFENSE:9
Block- Knocks some damage of enemy hits. (2pts)
Enchanted Armor- Significant bonus to Armor and MR. (2pts)
Unyielding- More damage reduction. (1pt)
Veteran Scars- Some bonus health that can help early when you are squishy. (3pts)
Juggernaut- Pretty good increase to health that can make a difference. (1pt)

As jungle Aatrox I switch my defense masteries to the following-
Recovery- Increases your health regen in the jungle (2pts)
Tough Skin- reduces the damage you take by monsters. (2pts)
Veteren Scars- Same as above. (3pts)
Bladed Armor- Helps clear camps faster while you take less damage. (1pt)
Juggernaut- Same as above. (1pt)

Marks- Armor Penetration- With the armor pen rune, stops you from having to rush or even get an armor penetration item. I prefer these over flat ad because your going to be using your E alot early instead of auto attacking, for msot lanes.

Seals- Armor- Decent amount of extra armor to start, so that you take a bit less damage.

Glyph- Scaling Magic Resist- The only time these are worse then flat MR, is when there is an AP top. In the case of an AP top, just outlast them, until your MR starts catching up.

Quintessence- Since you don't have AD marks, you want AD Quints just so that you have some AD, instead of none.

Normal start-
Get leash by nearby lane at Krugs, smiting it for buff.
Move on the red buff, using a pot along the way.
Grab Raptors
Recall
Go get blue
Kill Gromp with Smite
Do Wolves
Do Raptors/Krugs again if they are up
Gank a lane if necessary
Continue Farming untill you have enough for devourer
Stack devourer, ganking when necessary
If bot and mid enemy champions are back, go for dragon

For ganks-
Gank a pushed lane (pushed by the enemy team that is)
Initiate with QE combo and auto attack while zoning them from turret if you can, get your laner the kill, or take it if he cant get it.

Most match up information is listed above. I will add significant information ,that i may have missed, here at a later date.

Champions that i find work welll with Aatrox-
Yasuo- Your q can be a knockup and is very good for initiating fights with him.
Sona- Her heals can keep you in teamfights
Soraka- Same as Sona
Other hard cc champions work well as well, since they will stop the enemy from escaping while you finish them off.

Your primary combo as Aatrox is Q -> R -> E -> Auto attack while casting Hydra. If you have a BoRK, use it right after you R.


Laning-
You will want to walk around, auto attacking when you have a chance, and casting e to do some damage to enemy champion, or to zone them from farming. Certain champions will be able to zone you out. In this situation just sit back and use your e at smart times to get 2 or more minions if you can. I generally bring the minions under turret, as it is unbelievably easy to farm with Aatrox under tower.


Team fights-
As Aatrox you have an ability to go straight over the enemy team, or a wall, that is separating you and the enemy carry. If you can get to them with combo, you can destroy them. Just don't dive into a situation in which you will die.