Events in Yuki's life have let her become privy to this secret world. At a young age, she was attacked by a vampire. Just before she was about to fall victim to him, she was rescued by another vampire, Kaname Kuran. Because of this early experience, Yuki does not fear vampires, but she does realize there is a line between their kind. It also gives her a delicate relationship with Kuran, a person she loves and admires, but cannot pursue. Add to this the fact that Yuki is also the school headmaster's adopted daughter, and a member of the school's disciplinary committee, and you've got a girl with a lot on her plate.
A third key character is Zero Kiryu. Yuki and Zero met as children, though Zero's story is a bit more tragic. He witnessed his family being slaughtered by a vampire, and therefore holds a bitter grudge against all vampires. He holds it at bay, and manages to perform his duties as the only other member on the school disciplinary committee.
Maybe it's a little confusing to talk about disciplinary committees so much without explaining exactly what that means in this story. Basically all the vampires are tragically gorgeous, and so all the girls in the day class form a wild mob whenever day and night classes change places. Yuki and Zero try to keep the students separated so that there are no vampire related incidents and so that no one discovers the secret.
I do have a bit of a problem with some of the action scenes, probably because I've watched the anime first. Some of the action is unclear, and doesn't seem as forceful as it should be. For example, there is a scene where Kaname strikes one of his fellow vampire students, but it's confusing as to just what happened. There are other typical (and forgiveable) problems with proportion, but other than that, the art style is satisfying, quality stuff by Matsuri Hino.
This is a solid first volume for what is shaping up to be an interesting story. The main characters work well together. Kaname is the gracious, handsome vampire that Yuki can never have, while her partner Zero is brooding and quiet, and keeps himself at a distance. A bit of sexual tension builds and you also get one of the satisfying "twists" in the story at the end of this volume, so don't think that this is simply a set-up volume.