Hello! This is my guide for playing Aatrox. Aatrox is a solid pick with a lot of damage control. Let's first talk about his abilities. Deathbringer Stance is going to let you:
Aatrox's next basic attack gains 50 bonus range and deals 5-12% of the target's maximum health as bonus physical damage (depending on level), while healing Aatrox for 100% of the bonus physical damage dealt (reduced to 25% against minions). This damage is capped at 100 against monsters.
(https://www.mobafire.com/league-of-legends/ability/deathbringer-stance-886)
Deathbringer Stance's cooldown is reduced by 2 seconds whenever Aatrox hits at least one champion or large monster with a basic attack on-hit or an ability. The cooldown is further reduced by 2 seconds if he hits with the Sweetspot of The Darkin Blade.
Absolutely solid against many champions. If you hit your third Q, you are getting even more cooldown! It's a mini BOTRK passive that is lowered cooldown when you are fighting.
Let's check his Q:
Aatrox swings his greatsword in the target direction, striking enemies in a line. The Darkin Blade can then be reactivated twice within 4 seconds, with the second cast refreshing the timer. The second cast strikes enemies in a cone and the third in the target area.
(https://www.mobafire.com/league-of-legends/ability/the-darkin-blade-887)
The first cast deals 10 / 30 / 50 / 70 / 90 (+0.6 / 0.65 / 0.7 / 0.75 / 0.8 per attack damage) physical damage, increasing by 25% on the second cast and 50% on the third. The Darkin Blade deals 55% damage to minions.

Hitting enemies at the far end of the first two casts and the center of the third deals 50% bonus damage and knocks up enemies for 0.25 seconds. Monsters are knocked up for 0.5 seconds instead.
Main thing to note: Less damage to minions. You are using this for fighting.
How about his E?
Aatrox heals for 20 / 22.5 / 25 / 27.5 / 30% of the persistent post-mitigation damage he deals against enemy champions, increased during World Ender.

ACTIVE: Aatrox dashes in the target direction.
(https://www.mobafire.com/league-of-legends/ability/umbral-dash-889)
Umbral Dash resets Aatrox's basic attack timer. Umbral Dash can be cast during his other abilities without cancelling them, and vice versa.

Umbral Dash may cast across terrain with an increased dash range. This may upscale his dash speed so that the dash takes the same total time as the standard maximum-range dash.
This ability is by far the most important for Aatrox because you are healing all of the damage and giving back some. Key word: You only heal after armor, so you ain't healing against tanks very much. Mainly useful in all ins with your Ultimate, World Ender.
AATROX'S EARLY GAME:
In early game you are going to want to prioritize itemization heavily. Certain components that Aatrox can rush include Hexdrinker (for Teemo), Bramble Vest, Boots, and maybe even a Kindlegem/Phage for the mediocre lanes. You don't want to be pushing too hard on Aatrox since mainly you can get bodied way too easily. Aatrox can heal as long as he is fighting constantly, so avoid getting kited early. Aatrox not only deals good damage, but he also has good CC. His weakness? He can't hit his abilities and he won't do much. Most champions are looking for direct hits, but with Aatrox the MORE direct the hit, the better. Let's take an example: Teemo. Teemo is a very annoying champion for Aatrox to face, mainly because of his DOTOT and his shrooms. If you try to 1v1 him you are taking him for granted. Teemo does too much damage to Aatrox, and he will almost defintely bring ignite. With an early CS lead, however this is an easy lane.
MID GAME:
This is when Aatrox peaks. You don't call Aatrox Aatrox without mid game in his name. In mid game, Aatrox will be dealing all of the damage, calling all of the shots, but still losing to Singed. This is when you outscale pesky laners like Teemo but fall far short of beating your hardest counters. Look for objectives. In the enclosed space of Baron Nash and Rift Herald, no one can contest you and your jungler two v two, especially with Sej or Rek'sai. Don't worry too much about farm. As long as you secure an early CS lead, now is the time for Kills. Aatrox can't chase people very well, but he can secure damage counts and CC for his team. He's like a basic Tank except without all of the explanations. Aatrox's damage is legendary mainly for the fact that he doesn't care about CC. Although Aatrox doesn't care about CS he still needs a lot of Assists. Rift Herald is an early and easy pickup, especially if you are in a Bully Lane, for example against Sett or Renekton, getting plates will make your life a lot easier. Although you can't hard carry like Master Yi, people are going to be forced to itemize against you.
Common things people are going to do to counter your healing:
Buy Mortal Reminder. Go ignite cheese top lane for a early lvl 3 kill with their jungler. Play Teemo. Go HP draining/HP burning champions. Play pesky high mobility champions that will put you to sleep 24/7. Rush Morellonomicon. Deny your TPs. And finally, worst of all permagank you early game so you can't get fed. Early Game is 100 percent Aatrox's bane so you have to win early. It's just that simple. There is not much to talk about in Late Game. You are mainly going to be a Tank and constantly bodyblock threats to your ADC. Aatrox is a bit special from other heal drain tanks like Mundo and LeeSin in the sense that he doesn't heal at all from self-healing, nor does he have any sort of shield. Aatrox is only TANK WHEN DOING DAMAGE. This means hitting their frontline Maokai makes you more useless than Yummi in teamfights, and is thus not encouraged. But 1v1's with Bruisers are extremely encouraged. Bottom Line? Aatrox plays like an Assassin. Lock onto one squishy/bruiser target that you can heal off easily and chase them down to get a reset off your ultimate to get more healing. Yes, you can try to hit multiple champs and 1v2 like Renekton but he gets kited too easily for that. Post damage mitigation is what allows Aatrox to be Aatrox, so you have to deal damage and hit all of those spicy Q's.
AATROX ON HOW TO PLAY WHEN BEHIND>
Your team is 10-24. You just got demolished by their Teemo and you are looking for revenge. All you have completed is your basic Goredrinker at 20 minutes. What do you do? A common thread would be to just CS and hope that mid game comes around in your favor -- but this is wrong. The correct play is to go off of your Bot/Mid Lane and try to snowball them correctly with your Jungler. Aatrox fundamentally needs a strong team in order to win a League of Legends team. A good damage dealer gives Aatrox the Battering Ram to the Castle(enemy champion), since if Aatrox gets focus fired too heavily in a fight, he will easily die. Aatrox's damage is absolutely fundamental insane because of Armor Pen. However, he doesn't acutally have any armor pen built into his kit, so how do you deal with dat? Simple. You buy some. Black Cleaver isn't as good right now so I suggest Serylda's Grudge -- it gives you damage and ALLOWS you to chase practically anybody because of the slow. Super useful because of the ability spam, however absolutely worthless against Mundo, one of Aatrox's hardest counter. Percentage HP damage destroys Aatrox, so the only play for Mundo and other champs is to go the DD-> Spirit Visage Barrier Tech and play for your team. As long as you heal against those champions, whether or not they take CC is irrelevant. You're not gonna care anyways. Mundo doesn't do just a lot of damage, other champions like Jax and Fiora can also out CC and outscale you. The biggest problem, though is that they can set up huge dives and put you massively behind. This is why a lot of people compare Aatrox to Nasus - you do terrible early game, but mid game as long as nobody messes with you it's a free win. However, get messed with and you are looking at a loss. This is where coordination with your jungler comes into play. Invade with your jungler, set up some wards, secure Rift Herald and Drake prio (If your bot is winning. If your mid is winning play for roaming into Mid) and try to win early. Aatrox is a very good top laner pick in this meta because he benefits hugely from items. Hit one powerspike and you will be good to go. Aatrox does loads of damage, so even at low hp as long as they dont have ignite or you have a support like Lulu you will be fine. you can come back, heal up and go 1v9 as Aatrox depending on enemy team comp. First picking Aatrox is ill advised because he is not a good first pick. Enemies can easily counter you and pick burst resistant champions like Malphite and kiting champs like Vayne. If you have a jungler and you are first pick, ask to switch with him and then the enemies will think twice about blind picking into you, especially if they know you are a one trick Aatrox player.

https://na.op.gg/champions/aatrox/top/build

op.gg of aatroxplayers:
https://na.op.gg/summoners/na/Archangel%20Aatrox
The best.
https://na.op.gg/summoners/na/Bruisers%20Only
Hullbreaker Aatrox.
https://na.op.gg/summoners/na/Astaroth420
Aatrox player that switches between many items.
https://na.op.gg/summoners/na/Sardaukar%20Elite
Tank Aatrox player that cheeses early with Ignite.
https://na.op.gg/summoners/na/A%20World%20Ender
Very good Aatrox player. Is a heavy Maw, DD and Serylda's enjoyer.

potential bans: Malphite, Teemo, Jayce, Ziggs, Brand, Draven, Karma, Syndra, Varus and Viego.

https://docs.google.com/document/d/11XDoluKqe5MH0CfdAy2jV2XWuy9mGPC10MkODu7KEbw/edit?usp=sharing

Thanks for stopping by!
other guides:
https://www.mobafire.com/league-of-legends/build/tristana-domination-easy-freelo-with-minecraft-cannons-610008