Most of Aatrox matchups are skill dependent which makes him a great blind pick.
Only high mobile fighters that can run Ignite are a real threat to him in lane.
If you are more experienced you can almost but all other matchups in "Even" tier at least when it comes to winning lane.

2nd Item:

Profane Hydra really helps with wave clear and therefor enables you to push in your wave faster and look for plays more often. Its a great choice 2nd especially when you dont have a lot of kill preasure on your laner or it is just not that impactful to look for a solo kill on him (often the case against champs that dont scale that good/ arent a threat on sidelane). Most of the time I go for it because its great for building/extending your lead and play to carry the game.

Sundered Sky also good and synergies great with your passive. I like to build it when I dont think there will be a lot of skrimishing in top river with my jgl and mid (when jgl only plays for bot for example) and I have more impact by keeping my laner from scaling than by trying to solo carry.

You can go Serylda's Grudge 2nd against tanks like ornn if you like but I think hydra is better in most cases.


Rest of Build:

Serylda's Grudge as 3rd or 4th is good if your facing champs with higher armour and the slow is very good to ensure your Qs land on low hp targets.

Sterak's Gage is also a very good choice as 3rd or 4th item. The shield from the passive really helps with turning around fights.

Go Death's Dance 3rd if they have a lot of AD if they have a more balanced team comp damage wise you can pick it as 4th, 5th or 6th.

Spear of Shojin is a viable item but other options are just better in most cases on Aatrox so you shouldnt build it.

You can pick Spirit Visage as 5th or 6th item if they have a lot of AP (for example a fed mage mid that can just oneshot you). If the enemy top and jungle are AP you can also build it earlier. Its the only tank item i would recommend with this build, because the build relies on you dealing a lot of damage and carry your team.
Serpents fang is a really niche item but if the enemy team have a lot of shields that prevents you from picking their carries its an option.

Maw of Malmortius is only an option if the enemies are full almost full AP and spirit visage alone isnt enought to prevent them one shoting you. You shouldnt build it else because then you cant build sterak which is just very strong on aatrox.

Hubris can be strong if you completely stomp the enemy team but in that case what you build hardly matters anyways. In 99.999% of cases its troll.

You go Chempunk Chainsword as one of your last items if you had to rush executioners calling in a machup like fiora. In most other cases you shouldnt be the one in your team building antiheal.

Go Guardian Angel last if the enemy team can all-in and one shot you.

• dont leash your jungle: you just give your opponent a chance to exploit you and throw away the chance to exploit them
• track the enemy jungler where does he start? what of his camps is up?
• dont die: if your dead you have 0 pressure so get as few deaths as you can
• dont tilt: its just a game and your jungler simiting your canon isnt the end of the world
• think about win conditions and game plan: during champ select and laoding screen you can already think about what you will need to do to win this game.
• dont depend on your team: no matter whats your ranked you always have to expect your mates to do stupid things, so dont expect much of them and play to maximize profit regardless of their actions
• consider full muting the chat: the chat has no real benefit and can potentially tilt or distract you

Because I will also give more detailed describtions of a few stratgies I will mark the most basic information red.

On no other lane is wave control so important as on top.
By correctly controlling your wave you can punish opponents mistakes, create huge leads and completely prevent your opponent from playing the game.
Wave control is a complex topic that you will only truly master by playing a lot of games but i will give you a brief overview on the most essential points.
This is a hard to explain just with words so I will try to use pictures as much as possible but if you want a more in-depth guide on it there are good YT videos on the topic. I really recommend "Coach Chippys" videos for the topic and in general (I swear Im not affiliated with him in any way but his videos really helped me out).

Here are a few key definitions:

Pushing:
Pushing is when minion waves move more towards one side of the map.
This happends when one minion wave is stronger than the other, either by one player damaging the wave more than the other, or one minion wave being bigger than the other.
If two equal minion waves meet up more towards either side of the map (lets say its more towards your side) the wave will push in the other direction (towards the enemy side) because your next minion wave will arive earlier.
(source:my fabulous drawing skills)

The diverence in strenght of the waves(and how much you damage it more than your opponent) determins how fast the stronger side moves towards the other.
If one side is only slightly stronger we call it a slow push.
If one side is much stronger (for example if you kill the enemy wave very fast) its called a fast push.


Crashing:
When you push your wave into the enemy turret its called crashing the wave.
If you do this you open a window for yourself where you can do things(like recalling roaming or diving) while your opponent is stuck under tower if he doesnt want to loose a lot of CS.
The bigger the wave you crash, the longer this window.
So always pushing in your wave when you can as fast as possible is not really that good because the window you get from a single wave isnt that big.
Here becomes slow pushing a thing.
If you only last hit the wave as late as possible, your wave will slowly build up and then you can let it crash.
One of the most common aproaches for the first waves you can do if you are stronger than your opponent, is to hit the first two waves in the game only slighly more than him, and when the 3rd(or 4th) wave arrives, you clear his wave as fast as you can.
If you want to crash your 3rd or 4th wave in this case depends on what exacly you want to do with the window you get.
If you are low HP/mana or the enemy jungler is pathing top(when he started in his bottom jungle) and your jungeler doesnt, it can be a good idea to crash wave 3 and then recall (this is called a cheaters recall). This way you avoid getting ganked, refill your HP/mana and can buy a long sword(in most cases).
You will lose 2-3 minions and therefor hit level 4 after your opponent so dont default to this trick.
crashin on wave 4 is especially good if your jungler is pathing top, because during the time you do so he will most likely be done with his fist clear and moveing into river to take rift scuttler. You can look to help him if the enemy is constesting it.

After you crashed your wave it will slowpush into you.


Freezing:
Freezing is when you get the wave into a state, where it stays in one location of center of the lane for multiple waves.
This is usually done by holding a few caster minion that remain from the last waves in a certain position.(source:https://mobalytics.gg/blog/wave-management/)
This picture shows how much of an minion advantage you need to freeze the wave at a certain location (its shows botlane but its the same for top of course).
If you freeze the wave near your turret you can zone of the opponent from the minions and making him more vulnerable to ganks.

Dont let the enemy bait you into using your Qs onto the full wave on wave 1 and 2.
If you do so your wave will crash into tower and he can freeze
the wave in front of his tower(if the enemy has strong AoE spells like Darius Q or Jax E you can try to bait them this way).
You are weaker on level 1-3 than most other toplaners so they will push the wave into you most of the time.
Try to hit the wave only slightly less than your opponent so it doesnt crash too fast(except when you are going for the trick i explained earlier).
If your opponents wave is not too big you can look for a freeze.
If your lane is pushed in like that it makes it very easy for your jungler to gank if he paths top.
Generally in most matchups you play rather save until level 6 and only go for short trades when your passive is up.
Level 6 is a huge power spike for you so you can really start looking for solo kills and skirmishes around that time.
Help your jungler on top side and even look for ganks mid and flank Teleport on bot to build up a lead on your opponent.

If you are not very behind now is the time to shine.
You fall of pretty hard in late game so try to have as much impact during this time as you can and build up a lead if you can.
You are not the best sidelaner but at least descend so look to pressure the enemy team as much on sidelane as possible but always be ready to move to teamfights so dont wander to far off.
You have great wave clear so push in waves and take jungle camps to build you lead.
You have a lot of mobility with your E and one way to use it is to jump over walls to catch opponents of guard.

Most toplaners can create more pressure than you on sidelane but because of you wave clear you should be able to contest them alone so your team doesnt ends up in a nubers disadvantage.
A lot of champs outscale you so rather look for teamfights than trying to get solokills.

Your job in teamfights is usually flanker.
That means that you approach a teamfight from the side or back to disrupt the enemy, catch out of position enemies and draw as much of their resources to you as you can without dying.
Use your E to create unexpected angles by jumping over walls.

Especially with the black cleaver build it can also be an option to play more of a front-to-back style if your team doesnt have a good frontline.
That means you stay with your team, in front of your carries and focus their frontline first.