Saya Kisaragi is a kindhearted, if somewhat clumsy, student who trains by day to perform standard religious duties at her father's shrine—but she becomes an unstoppable, monster-slaying swordswoman by night!
Its important to remember that this manga is predicated on two things:
1) This was originally an anime series (of the same name).
2) This is part of the larger 'Blood, the Last Vampire' universe
If you're going into the manga having watched the anime, read/seen previous incarnations of the universe (Blood+ for instance, which is both an anime and manga domestically available in America) or a combination of the above, your mileage will vary from my experience. For me I've only seen one episode of the anime Blood+ and the live action movie (which...if it wasn't for the British actors I probably would not have seen that movie).
The animated version of Blood-C feature character designs and concepts from CLAMP and Ranmaru does a good job of mimicking that style. A really good job, which unaccountably disappointed me. From the art images I've seen of the anime vs this, Ranmaru didn't change very much. A few details here or there, but nothing to really make it stand out as her own. It does manage to avoid the pitfalls of soulessness that other anime to manga adaptations seem to have. (Yu Kinutani looking at your Motoko Kusanagi artwork).
If the above synopsis is vague, its because the first volume is mostly set up for later stories. At least, that's how it feels. We meet Saya, her father (who tends a Shinto Shrine), Fumito (an old family friend, who runs a nearby cafe), Yuka (Saya's leveled headed best friend), Nene and Nono (identical hyperactive, slightly ditsy, twins), Itsuki (polite, affable classmate who has a crush on Saya), Kanako-sensei (their...slightly shady teacher) and Shinichiro (quiet, mysterious, loner classmate).
That's a lot of people. Thankfully they're all easily distinguishable and have interesting (if well traversed) personalities. Content wise, the four chapters are fairly episodic, with a monster of the week appearing. Only one is really important, when she meets a talking 'Ancient One' (which seems to be the phrase for supernatural creatures) the plot picks up at this point though we're still left with a LOT of questions.
Saya goes from complete klutz to crazy sword-wielder when she picks up the blade, which was left to her by her mother (also a crazy sword-wielder). I'm not entirely certain if her Klutz persona is a put on, or if the blade somehow empowers her or what however.
In all this was an okay read for me. I think I'll picking up the anime though because honestly? Waiting to find out what's up with the 'covenant', the shady teacher, Fumito, Shinichiro...well. Hey I'm impatient you know?