If you’re familiar with Sara Gran’s Claire DeWitt mysteries, I need say nothing more than this: The third novel in the series, “The Infinite Blacktop,” has just been published. For those who ­haven’t yet read Gran, trust me, you are in for a singular mystery experience.

Gran’s heroine, Claire DeWitt, is one part Auguste Dupin, one part Jack Kerouac-type “Dharma Bum” and allover nasty woman on a mission. The world she inhabits as a private eye is traditional (mean streets, duplicitous clients and an atmosphere of cosmic fatigue) and, yet, so weird that her cases seem like they’re taking place on one of those old Anytown, USA, “Twilight Zone” sets. “The Infinite Blacktop” is the most intricately plotted of the series. It’s pretty standard for mystery novels to feature two parallel plots that ultimately converge; here, Gran ups the ante by concocting three stories that take place at three different stages of her detective’s life, culminating in an ending that, in trademark DeWitt fashion, leads to only more questions down the road.

Of the trio of plotlines, the earliest and most compelling one dates from DeWitt’s childhood in the crime-ridden Brooklyn of the 1980s. Claire and her two best friends find each other in fourth grade, bonding on their shared obsession with the adventures of “Cynthia Silverton, teen sleuth and girl detective.” (Think Nancy Drew except, like DeWitt herself, weirder.) Inspired by their reading of the monthly comics, Claire and her girlfriends begin solving actual cases that stump the NYPD. Then, one night, one of those friends disappears from the Brooklyn Bridge subway station. Two decades later, the adult Claire ruminates on the long aftermath:

“I became the best detective in the world, just like I’d dreamed of. I met kings and I met magicians. . . . I met people who had everything on earth except the one thing they wanted the least but needed the most — the truth.

“I solved every mystery I came across.

“Except my own.”

But, now, there may be a break in that most personal of cold cases. One day in 2011, the adult Claire awakens on a highway in Oakland, Calif. Claire’s car — a tiny Kia that she rented while on assignment — is now a pile of twisted metal. As her memory fitfully returns, Claire recalls that another car, a big white Lincoln, deliberately rammed into her. Thinking about who might want to kill her, Claire recalls something else: A few days earlier, she’d located a rare-book dealer who owned a complete set of the elusive Cynthia Silverton comics. On a whim, Claire had answered an ad in one of the old comics that offered a “home-study course . . . to earn your detective’s badge from the comfort of your own home.” She’d sent her application to an address in Las Vegas; abruptly, Claire now realizes that the Lincoln that smashed into her had Nevada plates. Without hesitation, a bruised and bloody Claire hustles away from the accident scene and heads toward Las Vegas, stealing credit cards and false ID along the way. She’s determined to find her potential killer(s) before they can ambush her again.

Set chronologically in the middle of these two story lines is what seems to be a less personal case dating from 1999 in Los Angeles. Back then, Claire was young, broke and adrift. Eager to earn her PI license, she accepts the challenge of taking on an LAPD cold case involving the suspicious deaths of two artists. This tale, too, ends up circling back to the Zen-like lessons from those Cynthia Silverton comics, as well as from the other lodestar of Claire’s professional life, a slim book she also first read as a teenager called “Détection,” by the legendary French detective Jacques Silette. As Claire says of reading “Détection”:

“It was a spell. A virus. . . .

“Other books would give you ideas and words and things to defend and argue. Détection gave just one thing — the truth — and in its short 123 pages (US reprint edition, 1959) offered us 123 different doors to the same place: each door locked, each ready to be picked open if you worked hard enough.”

The peculiar charisma of Gran’s mysteries derives not only from her wayward plots but also from eccentric details such as those quotes from the philosopher detective, Silette; detailed excerpts from those slightly sinister Cynthia Silverton comics; and even the tantalizing titles of the other cases Claire references: “The Clue of the Watercolor Butterfly,” “The Case of the Bitten Apple,” “The Case of the Broken Lily” and “The HappyBurger Murder Case.” In time, those of us who’ve fallen under Gran’s spell — or should I say, caught the “virus” borne by her books? — hope to read about all those cases and more.

Maureen Corrigan, the book critic for the NPR program “Fresh Air,” teaches literature at Georgetown University.

THE INFINITE BLACKTOP

By Sara Gran