This isn't the anime's source material, although it predates it by a year. It's just another adaptation. Kore wa Zombie Desu ka? (aka. Korezom) has appeared in the following forms:
1. Light novel series (19 volumes) 2009-2015
2. This manga series (8 volumes) 2010-2013, although there are several other manga also set in the same universe
3. Anime series (25 episodes) 2011-2012
I'm mildly tempted to buy the other seven books, since that's not a long series and I quite enjoyed this volume. However I probably won't. After having seen the TV series, it's a mixed bag and I don't feel the need to experience it in stereo. Tomoko isn't a fan either, although that's unsurprising since this kind of show isn't to her taste. She tried reading it and gave up after 25 pages.
The set-up's just like the anime, unsurprisingly. Aikawa Ayumu is a zombie who's been resurrected by the necromancer Eucliwood Hellscythe, aka. Yuu. She's one of the three girls he'll be living with, along with Haruna the Magical Garment(-shedding) Girl and Seraphim the vampire ninja. There's also cross-dressing with a pink chainsaw.
The manga's main problem, compared with the equivalent anime episodes, is that it's more clearly focused on harem fanservice. The first four pages are basically one big panty shot of Haruna as she falls out of the sky. This kind of thing continues. The manga seems to think its main selling point is showing her nude or scantily clad. Indeed, this volume seems to think Haruna's the main girl, despite also telling us everything we need to know about Yuu. Unfortunately:
(a) Haruna's obnoxious (albeit also amusing),
(b) Both Haruna and Yuu look younger than I'd expected. It's quite a subtle thing. They're basically the same as in the anime and it's hard to identify specific differences, but I do think they look younger. In the anime, Haruna to me just seemed short and Yuu came across as a mysterious magical entity of unknown age. However the manga's Haruna is a pitch to the lolicon audience, especially given how often she's naked for fanservice purposes. The only redeeming feature is that it's Barbie doll nudity, so there's nothing to see. Meanwhile Yuu is just a teenage girl. She looks younger than Aikawa. I'd be happier if they revealed that she's really an eldritch abomination who's been alive for millennia, which is actually very possible but I'm not really expecting it.
That said, though, I think it starts its story better than the anime did. Admittedly I think the anime begins badly, but what we have here works. I felt I was reading a lively, entertaining comic strip with cool stuff happening (although I wasn't keen on the Haruna fanservice).
It's quite a compressed adaptation. The mangaka's skipped quite a lot in order to focus on what he sees as the core story. Eight volumes isn't many. All four main characters are already together by the end of chapter one and this first book gets as far as the anime's ep.4.
Despite this, though, I think there's more to the characterisation than there was in the equivalent anime episodes. Haruna's actually quite funny, with her overreactions, worldview and misunderstandings. As for Yuu, we see more of what she likes, e.g. Steven Seagal and watching variety TV shows. (Does she like the former because she finds his films exciting, or because she doesn't and she's trying to avoid emotions like excitement? Either way, it's surreal.) She's a bit more eccentric here than in the anime, I think, and is often drawn with Blank Cartoon Eyes that make her seem like a comedy character. She can be quite a chatterbox with that pen and notepad. At the same time, though, it occurred to me here for the first time that Aikawa's habit of talking to the imaginary cutesy Yuu in his head might be a mental reaction to the psychologically unsettling situation of talking to an emotionless person who won't even speak to you. That seems quite likely, actually. Aikawa doesn't fantasise like that about the other girls, after all.
Mind you, the Imaginary Yuu spots are all silly moe stuff and it's hard to maintain any serious interpretation of them. That doesn't mean the reading's not available, though. Oh, and I'm not sure how Yuu's powers are meant to work. Is she like Jesse Custer from Preacher? The implication is that if you can't hear her words, they don't affect you... but I'd always assumed she was powerful enough to affect inanimate objects too, e.g. that tree she blasted once. The dead aren't known for listening too much, for a start, and we know she can resurrect things. She's a necromancer. I'm probably being unfair, but I'm not convinced yet that all the ideas in this show quite fit together.
This volume gives Seraphim gets much less of the spotlight than the other two girls, but that's fine. It's not as if she's that interesting anyway. I did struggle with some of the fonts, though. Reading Japanese isn't easy to start with, without the lettering making it even harder.
Would I recommend this book? I don't think so. The ideas are pleasingly wacky, but the Haruna fanservice and the harem set-up in general are reasons to avoid it. So far, though, it's quite fun, it has some deeper stuff going on with Yuu (and to a lesser extent with Haruna) and it appears to be less of a mess than the anime. Broadly speaking, if you're in doubt, read something else. There's tons of brilliant manga out there. You could read for years and not get to the end of it. However sometimes you hear of books or TV shows so out there that you know you have to experience them. This might be that for you. This book will show you an unkillable teenage zombie in frilly pink drag using a chainsaw to fight a three-metre-tall crayfish in a schoolboy's uniform. You don't get that every day.