This build is intended for any standard game. If you happen to be in a game where you face all AP champions you cannot blame this build or me if you happen to do bad with it. Personally this is my recommendation for this champion. I have played him many times in the last 3-4 days and he is now my main. This build is an Attack Speed / Tank build. The build focuses on ATK SPD so u can get more CS kills, more money, and gain health faster with your W. If you happen to compose and finish this build in-game even when your losing it can turn the game around. I was 9/10/9 before i finished it then when I finished became 20/10/9 end game. We all went straight mid and I tanked every champ on the opposite team. Even if they got me to extremely low health i would exchange my W and start regaining it super fast. Even when I didnt have my passive. One thing you have to remember though is that Aatrox by himself can be really squishy so you want to purchase armour and tanky stuff like warmogs.

Aatrox Pros/Cons

Pros:
Passive is the best ever
His E helps him secure kills
Q helps him gank
W is pretty much amazing considering u heal yourself
His ULT is Broken and when combined with more ATK SPD can destroy 5 champs

Cons:
Aatrox can be really squishy at times
Passive cool down is SUPER LONG
After passive is used he becomes extremely vulnerable
can be hard to play at times
hard to play against ranged champs such as vayne

When you farm with Aatrox you want to make sure you are not close to any enemy champs. Farming comes really in handy because of your W. Also when you farm you dont only have to farm off minions with aatrox's W being so broken you can farm anywhere except maybe Baron.
When farming a good idea is make sure you are always above half health. If not make sure you are as close to your turret as possible unless there is an easy kill close by.