Support Aatrox has strong early pressure and can easily double kill bot lanes who aren't prepared at lvl 6. Aatrox can punish immobile ADCs and supports very hard, his E+Q1+W+Q2 can easily lead to getting a flash or kill. He can set up ganks very well especially if you have a CC jungler. He can roam with jungles with weaker 1v1's to win 2v1 fights in jungle.
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The standard Glacial Augment page can be used in most situations and has good lockdown with your Q+E+W combo. This page is countered by champions with mobility spells such as Vayne, Ezreal, and Lucian. You can swap out Second Wind for Bone Plating into high burst ADCs like Tristana or Jhin.

The Aftershock page is best used for tank Aatrox or when into high mobility champions. It gives Aatrox much better all in potential at the cost of lockdown and peel potential for your carries. <currently cut for further research>

Support Aatrox's level 1 is very weak avoid walking up to the first wave as you have no reason to, try to contest bush if you are into a melee support with a viable lane ADC.

DO NOT USE SUPPORT ITEM STACKS ON FIRST WAVE!

Wait for the 2nd wave and use it on 2 of the melee's, assuming your ADC has arms this will allow you to get a faster level 2 which you can abuse if the enemy doesn't respect it in their positioning allowing you to E+Q1 poke or even all in if you have Glacial Augment into a winning matchup.

At level 4 you spike hard increasing your damage substantially, use this if your enemy is positioning poorly, this is an opportunity to all in when in a winning lane.

At level 6 you gain access to your ultimate which gives a LOT of movement speed which can be used to run down the enemy if the wave is on your side of the lane. This is where most even matchups turn around, casters than could bully you pre-6 will have to beware your engage.

Post 6 you should look for roams with jungle and ganks mid. This is especially important when winning lane as it allows you to extend your lead into other lanes.

Don't forget to use your E to hop over wall and deny blast cones when taking objectives. You can also use your Q over wall to harass junglers looking to steal.

Bruiser and Lethality Aatrox fall off post 30 minutes but Tank thrives late game. Late game you will either serve as your team's engage and will probably die for picks and 5v5 engages or if you have an engage jungler or top you can peel your backline with your CC and damage. Tank Aatrox can also use Redemption during teamfights for a burst large heal which can easily make the difference in a close fight, the best part about Redemption is that you can use it while you are dead meaning if you die as the engage you can still help your team.

I have created a Google Slides presentation that I paste in every champ select when playing this pick:

https://docs.google.com/presentation/d/1Z7IdtwvPFrpyrOViP-38vm9NY94_7neX7uxwOswv5k0/edit?usp=sharing