Oh sorry I haven't been checking my boards account lately lel.
Okay first of all... it's not really the build that makes a good Aatrox (although a good build will surely help you improve) a good Aatrox, it's how you play him that makes all the difference.
You have to understand that Aatrox is a gimped champion, you're basically putting yourself at a disadvantage playing him opposed to someone in the meta. If you want to take the (hmm... for lack of better word) 'bitch' route and build tanky then i'm sorry but you're doing it wrong.
As Aatrox, your goal is not to just merely survive... your goal is to destroy the enemy top laner, demoralise their team by splitpushing, draw aggro from all lanes and eventually seize the win with your own efforts.
So now that you know what's Aatrox purpose is - a snowballing, split-pushing, aggro-drawing monstrosity, you have to ask yourself how do you build for this? You know you want to snowball so what stats are going to help you obtain this state in game?
In my opinion, the best stats to go for are as follows:
AD, AS, Crit, Lifesteal, Waveclear
Okay now you know what you want, the next step is to think about the item options and which would be best suited from 1st to last item in sequence.
Personally for me, I highly value all of those stats... so you know what's the best two items that cover that entire list? 
and 
.
These two are my core items on Aatrox, it covers all of your early game and mid game needs whilst making you deceptively tank in a duel whilst giving you good waveclear to push and farm and crit to cheese your opponent.
For boots, grab whatever you need the most. If you're snowballing -> grab berserker greaves, if they have a hard hitting ad champ or a yasuo, grab ninja tabi if they have lots of ap, merc treads. Simple.
Now for the next three items... honestly it's going to be reactionary to the type of game you're having. If you absolutely shat on your opponent and they have no chance of even harming you at all in a duel 5 - 10 minutes down the line... then build yourself more damage. Something like a 
or 
against AP are great purchases because they not only increase your damage output, but also allow you to mitigate some damage. If you're finding yourself set on damage and the enemy team has some hard hitters on their team then that's when you pack on some resistances. There are two types of resistances, flat resistances if you think you think you are going to take periodic damage (damage in intervals) in which these items become paramount 
, 
and 
and what i like to call 'burst resistances' where you will receive a huge amount of stat or become immune to incoming damage after being bursted, for example 
, 
or 
(loljks don't buy zhonyas pls, ap aatrox is dogshit).
Once you have , , boots and two resistance items (it can be a mix if you like for example, + ) then the last item is entirely up to you. Personally I like to have 3 damage items so I would recommend one of these items to be fit in your final slot 
basically copying yasuo's cheesy build but you're less effective with it, 
more damage means faster enemy deaths but also more healing from lifesteal, more lifesteal and 'some' damage mitigation, exceptional against ap, (note: only buy maw or sterak by themselves, don't couple them together or you're wasting a precious passive - might as well replace one for something else) and finally 
just cause it's fun.
If you've listened to everything, your build should look something along the lines of this once you've reached 38 - 40 mins (hopefully you end your games before late game though because the longer the games drags on, the less effective your lead from snowballing becomes).
TL;DR - Play aggressive, don't be a bitch. You learn more trying to play aggressive and being assertive with Aatrox than playing and building defensively.
Build offensively. RAVENOUS HYDRA + PHANTOM DANCER ARE CORE. If you are snowballing build even more damage. Buy two defensive items after your build core or after you finish 3rd damage item. Good luck.
[slayer-pantheon-popcorn]
