This is a book about a time-travelling serial killer and a woman who survives her own murder attempt and sets out to catch him. The most interesting part is that she doesn't even consider time travel as a possibility (the book is set in the conventional reality), but gradually comes to accept it, based on evidence.
The weakest chapters of the book were the ones written from the killer's point of view. Those parts have a detached, distancing quality. I didn't get any clue as to the killer's motivation. At some point he feels forced by the House itself (a house where he lives that serves as a portal to different eras) to go murder all those women. But he does not respond like an ordinary person would if they felt compelled to murder someone. At the very least s/he would be upset and conflicted about it. Even more so if the urge was planted directly in their mind by a mysterious force. That should make anyone question their own sanity, but the murderer does not seem disturbed. He is very nonchalant about all that.
If the killer had been portrayed in a way that readers could connect with him (and yes, to enjoy a book you have to connect with the villains too; you need to get into their mind and understand why they do what they do, even if you don't find it justifiable), I would have added another star to the review.
It is in the victims' plotlines that the storytelling really picks up. Each of the eight murdered women were interesting, different, and vivid. They made the book worth reading. It quickly became clear why they were called the Shining Girls. Each of them was ahead of her time in some way, breaking the mold of what was expected from women of their time. In that way perhaps the House could be viewed as embodiment of evil reactionary forces of the world. But if so, that metaphor isn't developed in the book very well.
The story really takes off when one of the women survives the attempted murder and gets on the killer's trail; as level-headed as she is, she is eventually forced to accept the evidence that the killer might have traveled in time to commit murders. I really liked that she applies every ounce of skepticism to examine all the other possible explanations, and only after exhausting them settles on the seemingly impossible.
I will not reveal the ending, except to say that it was a quite confusing. Perhaps that was deliberate: time travel stories are very difficult to resolve in a satisfactory and logical manner. Once you start dealing with time paradoxes, there is no good way out. So even though the ending felt handwavingly dismissive and intentionally obscure, it doesn't detract from the story that much; its essence was about the journey, not the destination.
Rating: approximately 3.5 or 4 stars out of 5