Aatrox is one of my fav top champs, he's quite impressive when it comes to certain aspects, such as being able to ignore harass from many top enemies, such as gangplank, akali, and other bruising/harassing champs.

The blood thirst/blood price combination makes him a very versatile champion, since they allow him to have a pretty good sustain while on laning phases, but also allow him to dive and secure kills pretty easily with blood price activated (purple W).

The fact that he also doesn't need mana makes pretty obvious that in order to maintain a good harass and to be able to use skills frequently, Aatrox needs both health and life steal whilde building. That's why the core items all correspond to a good combination with his skills and ability cost mechanics.

Also, the Blade Of The Ruined King allows the player to guarantee the kills, either with it's damage or his slow, they give a greater chance for an aatrox player to get fed.

Spirit visage is obviously refered as a situational item, since it's UNIQUE passive combines like a charm with Aatrox's passive. Late game, it may be a turning item while on teamfights, since it provides Aatrox with massive amounts of health when his passive is active.

I obviously chose teleport and ignite because combining with Summoner's wrath mastery, aatrox may boost his abilities and damage to a point where it might be the first blood factor during a fight top. Teleport is used for either a fast return to the lane or to efficiently help hist teammates byt teleporting to a bot ward and helping to secure a kill. It is very important for Aatrox to have a farm advantage and being able to harass his opponent as much as porrible. Blades of Torment form a skill wich allow Aatrox to get last hits or distant minions and harass simultaniously.