Saya may have inherited her mother's ability to read minds, or at least to read body language. She grew up without her mother but Fumito, who owns the restaurant next door, cooks for her so that's almost as good. When Saya isn't busy being a school girl, it is her duty to slay the ancient ones, demonic people eaters that have existed since the beginning of time. In that regard Saya is following in her mother's footsteps, even using her mother's divine blade. Slaying the ancient ones is an important job (and of course it must be done in a schoolgirl outfit with a short skirt), but her duties do not prevent Saya from living a normal teenage life. Another plotline involves Japanese marshmallows, a missing baker, and a mysterious stray dog.
I haven't seen the anime series or film upon which this manga is based, nor have I seen the other Blood manga, so my impressions are based upon this volume as a stand-alone product. I like that much of the story concerns Saya's adolescent growing pains: her uncertainty about her future, her fear of leaving her home and her friends, her desire for social acceptance. She has a crush on a boy and her female teacher seems to have a crush on her. By issue 4, the battle with the ancient ones starts to come into sharper focus, but there are still a large number of unanswered questions. The story teases the reader with hints that there is more to the ancient ones than we know about, and we never do find out what's up with the missing baker. Saya keeps seeing hazy images of her mother so perhaps there's more to that story, too.
Although it's frustrating that the story is just getting its legs toward the end of the volume, the story is never slow moving, and Saya -- clumsy but kind in her schoolgirl life, an interesting contrast to her sword-wielding warrior persona -- is an appealing character, as are the story's secondary characters. I'm sufficiently hooked on the character and intrigued by the story that I'm looking forward to volume 2.