Aatrox is on the squishy side right off the bat, but has massive burst damage after he gets his ULT. Basically every time you engage, use your W and if you land it, follow through with R right away. This knocks the enemy(ies) into the air and sucks right around 1/4 of their health away instantly. If you have engaged with 1 or more friendly champs, it will normally be an insta-kill. If the enemy does manage to run (if they are fast, flash, etc.) engage them again with your E which will slow them down and normally give your W enough time to come back up, allowing you to re-engage (W) with stun, effectively removing any chance of them getting away. If they have gotten too far, flash is always a viable option, followed of course by your W and E.

My favorite thing about Aatrox is that he is just as good at running away from an unintended massacre as he is at initiating one. When you are on the run, most of the time casting your W over some trees is enough to thwart that unwanted 500 or so gold for the enemy team. If need be, his E coupled with his W and flash is an excellent way to get away from even the most determined enemy champs, although there's sometimes (as we all have experienced) just no way to run and you'll be a skull and crossbones on the mini-map for a little while.

This is my first guide, and I didnt know it was the consensus that incomplete guides shouldn't be posted.