The Shining Girls, By Lauren Beukes. HarperCollins, £12.99

To begin with, Lauren Beukes had an idea so perfectly simple it sounds like an elevator pitch: "time-travelling serial killer".

She then had the good sense to make it the premise from the start rather than the big reveal at the end. The crucial thing with good ideas is to let them breathe. Beukes does this: she doesn't make the mistake of trying too hard to make the house containing the door that opens through time to other eras make too much sense. This is a book about the paradoxes inherent in time travel – the things that make it more appropriately the subject of dark fantasy rather than science fiction.

Her other brilliant move is to make her monster stand for something other than himself. Harper is a derelict from the Depression, who talent-spots young girls in different decades and social classes, and comes back to kill them as adult women. He is both a real character into whose heart we look deeply – and are utterly repelled by – and a symbolic representation of the misogyny that has always stopped so many talented women fulfilling their potential. This is a novel about a serial killer which pays the correct amount of attention to his victims – African American, radical, lesbian, transgender and so on – so that in each case we care passionately that, perhaps, this one will escape him.

It is one of the rules of slasher movies that there always be the Final Girl. We and Harper meet Kirby on the first page. She survives him, and hunts him down, and works out that what is impossible must be true. Beukes knows how this story goes – the awful hipster boyfriend, the tousled older man, the feckless hippy mother – and she lets some of the clichés work out. She also has the sense to set the book in the early 1990s; Kirby with the internet would be far less interesting.

Beukes sets this novel in a wonderfully visualised Chicago over seven decades. This is a book about the death-duel of two fabulously realised characters, but she cares just as much about the others – of which the city is one. The Shining Girls is a finely organised, ingenious triumph.