As it turns out, THE INVISIBLE LIBRARY is pretty splendid. In a nutshell, the Librarians are in search of unique books, ones that only appear in one alternate universe, and are helping to keep the forces of chaos in line, all of which requires a lot of frenetic running around and adventuring and near misses. It's been pitched as Doctor Who with librarian spies, and while I didn't really get that vibe from the book, I do kind of get it from writing up a nutshell explanation, so. :)
One of the two things that really made it work for me was that our heroine, Irene, is a decidedly modern (even post-modern!) heroine in a job that often requires her to visit times, worlds and places that are not modern in sensibilities. The very slight clash of modern language & mentality against (magical) period settings made for a dissonance I really enjoyed. Irene was a lot better at playing into the rules of the eras than I'd be. :)
The other thing I really loved was the supporting cast. Irene's partner Kai was fine and fun, but it was the characters she met on her main assignment, the Great Detective type Vale and the Harried Inspector Singh, with whom I particularly fell in love. I've never even been a particular Great Detective fan, but I just love Cogman's version of the pairing, and I spent the whole last quarter of the book in despair because I could only see one way in which they could continue as regulars in the series, and I didn't see it happening at the end of the VERY FIRST BOOK.
It didn't happen, either, which is good, because it shouldn't have. But something else excellent did happen, and I'm really going to enjoy the second book. :)