Operation Abyss opens with you awakening to find a human body lying next to you, two dead bodies actually. You were on your way home from school when "something happened." You have apparently been kidnapped, by monsters. A strange man shows up to rescue you, but sadly he has to be rescued himself, by Alice Mifune. She’s an Xth Captain. The Xth are a highly classified secret group who do the actual work to dispel the variants for the XPD. The XPD are the official police force for "hazard cases." A hazard case happens when random parts of the city mysteriously turn into mazes that they refer to as Abysses. In them are Variants, monsters who attack normal people.
It’s not easy to keep an organization like the Xth a secret, but they are hidden deep under Hinowa Academy. Kenichi Kanzaki is the director of the Xth and he’s also the dean of Hinowa, which explains how they can hide the secret easier. The Xth members are recruited because like you, they all have Code-Rise. Code-Rise allows a normal human to activate powers that make them super-human. You don’t know you have Code-Rise abilities though, so you’re going to have to learn how to use them. There’s no better way than being thrown into the deep end to see if you can swim. Not long after you create a squad (you are given a "balanced" one to use, but you can vary it if you want), you are given a mission. Your squad is called Abyss Company.