“STARTED EARLY, TOOK MY DOG,” by Kate Atkinson (Reagan Arthur/Little Brown. 371 pp. $24.99)

“To the Pythagoreans, three was the first real number, because they saw it as having a beginning, a middle and an end,” says a character early in Kate Atkinson’s latest novel, the excellent “Started Early, Took My Dog.” Atkinson goes on to introduce three characters and interweave meditations on other sets of three — particularly beginnings, middles and ends.

Recently retired policewoman Tracy Waterhouse, a 50ish woman with no particular attachments and no plans for the rest of her life, has taken a job as security director of a Leeds, England, shopping mall, more out of boredom than anything else. Leaving work one day, she runs into an old nemesis, Kelly Cross, a “prostitute, druggie, thief, all-round pikey.” Kelly is dragging an abused toddler onto a city bus, and in a split-second Tracy finds herself asking, “How much for the kid?” An envelope changes hands, the bus pulls away, and Tracy is suddenly the guardian of Courtney, a solemn toddler she’d just purchased on impulse.

Meanwhile, former police inspector and private eye Jackson Brodie (returning from three of Atkinson’s previous novels) is wandering the English back roads, looking at the endless ruins of British civilization, trying to decide if all roads lead to or away from home. His split-second decision arrives when he sees a man brutalizing a small dog in a park. Brodie finds himself with a dog he’s not quite sure what to do with.

As Waterhouse and Brodie both get things they’re not sure they want, an elderly character actress is losing the one thing that matters to her: her memory. Tilly Squires, currently playing the mother of a detective on a cheapjack TV crime drama, is becoming known among her co-workers as “Ten-take Tilly” because of her failing faculties. When the producers finally decide to kill her off, sending her into retirement like Waterhouse and Brodie, it’s all Tilly can do to remember that she’s standing on a set and the woman aiming a gun at her is another actress.

How Atkinson interweaves these lives — in the past, the present and the uncertain future — is her particular gift as a writer, and her plot remains clear and straight even as she unfolds her stories at leisure. Along the way, she introduces threads from the past, including another lost toddler from a 1975 murder scene investigated by Waterhouse. All the tales tie together into a knot that’s complicated, elegant and completely satisfying.

“Started Early, Took My Dog” — the first line of one of Emily Dickinson’s simplest and most ambiguous poems — is as much an examination of the way we live as it is a suspenser. Waterhouse and Brodie both inhabit a world of iPhones and a disappearing middle class, finding themselves stunned and adrift on the sidelines of life, obsolete at 50 with nothing ahead but decades of make-work menial jobs. Both have seen too much to have faith in a world where the child abusers and dog torturers seem to be winning, and it has turned them slightly numb, with only occasional prickles of interest in being alive. When Waterhouse begins fantasizing about running away with her purchased child, re­invent­ing themselves as a proper mother and daughter named “Imogen” and “Lucy,” it’s a fantasy so tempting that she takes baby steps to make it happen, just to amuse herself. When she commits to the charade, she becomes Tilly’s mirror opposite: a woman who wants nothing more than to retreat into a fantasy world.

Waterhouse is a marvelously original character. When another aging cop sighs and tells her it’s a different world these days, “Tracy thought she must be missing something, it felt like the same world as ever to her. The rich getting richer, the poor getting poorer, kids everywhere falling through the cracks. The Victorians would have recognized it. People just watched a lot more TV and found celebrities interesting, that was all that was different.”

Atkinson’s dark wit and mastery at sketching connections — between people, places, times, things, emotions — are reminiscent of Ruth Rendell, and Atkinson shares that grand master’s facility in balancing cynicism, compassion and pragmatism. The result is crime fiction that’s also splendid modern literature.

Allman is a writer and editor who lives in New Orleans.