Aatrox: The Justicar of the Jungle
Champion Introduction
http://leagueoflegends.wikia.com/wiki/Aatrox
Runes -
9x Greater Mark of Armor Penetration
9x Greater Seal of Armor
9x Greater Glyph of Scaling Magic Resist
3x Greater Quintessence of Attack Damage
This is my suggested run spread for him. I actually ran him with Movement Speed Quints instead of Attack Damage when I played him, and it worked great, but the extra damage is nice as well.
Masteries -
I personally like this for Aatrox. The normal +30 HP from Veteran's Scars isn't really as important on Aatrox considering the amount of HP he'll gain back and the fact that when he dies, he doesn't. Also taking the turret damage so that he can help push in a turret after ganking a bit better.
Final Build -
Berserkes Greaves are the best option because boosting his attack speed is a must. The more he attacks, the more often he'll proc his Blood Thirst/Price. Choose whatever Tier 3 Upgrade you think will best fit the situation. If needed you can also get Mercs for the MR and Tenacity or Ninja Tabi for the Armor, dpeending on the enemy team comp and how well you're doing.
The Bloodthirster is a great item for Aatrox, especially when you're coming for unexpected ganks and such. Between Blood Thirst and life steal you'll be capable of jumping in and out of fights with no issues.
Ravenous Hydra is another beautiful item for Aatrox, because what's better than gaining life off of one enemy? Gaining it off of all of them asthey try and try to kill you, but you simply /laugh until they all die.
Blade of the Ruined King's passives are a great addition to Aatrox, giving him another way to get some HP back, MORE life steal AND that attack speed I've been talking about.
You might be wondering 'why Trinity Force over Phantom Dancer?' and I'd respond to you with all of the things it gives him. More Attack Speed, more Damage, a bit of AP to add a small oomph to his E, a bit of crit as well. Now add in Icy, letting you slow down and keep up with any enemy who wants to run away, and Spellblade allows for a nice chunk of damage after using his Q to knock up your enemies, or E to slow them down. It also gives HP which is quite useful. The only useless bit on it is the Mana, but I think it's worth it overall.
The Warmogs can be subbed out for either a Thornmail or Spirit Visage is you believe your regaining HP enough and wish to have Armor/MR, respectively, instead.
Summoner Spells -
Flash?ignite is standard on most junglers for me, though I'd be willing to swap out Flash for Exhaust because his Q allows him to jump at an enemy.
Overview of Aatrox:
I personally see him having great Ganking potential, be it form the jungle or in lane. His Q allows him to not only jump into a fight, but knock the opponents up if aimed correctly, giving your teammates some nice time for free damage. In order to maximize your W's worth I like getting plenty of attack speed, it's even better when he's below half health because it's healing goes up by 200%! Then, once you have enough life steal or you think you can easily take an enemy without needing the HP Regain, simply switch to Blood Price, and watch as their health melts away. Aatrox's E is quite Aatro-cious in my opinion. The little bit of AP that Trinity Force gives you will give it a little extra punch, but the range is too short and the slow isn't that great on it's own. Massacre is a great Ultimate to initiate and win teamfights with. First, jump in with your Q, then Ults, taking 15% of every enemies HP around you, then gain that HP on top of your current max AND gain a ranged attack (325 range) for 12 seconds. Just fantastic.