Jay R. Tunney, the author of “The Prizefighter and the Playwright: Gene Tunney and Bernard Shaw,” says researching the book gave him a deeper understanding of what the Irish bard’s relationship with his father was about.

“The Prizefighter and the Playwright: Gene Tunney and Bernard Shaw (Firefly Books, $35), by Jay R. Tunney: An improbably handsome ex-Marine devotes himself to a career of battling thuggish brutes in the prize ring, and one day gets up off the canvas to score a storybook comeback and retire as the heavyweight champion of the world.

Between bouts, the former “poor boy from the docks” and high-school dropout spends his time plowing through libraries of classic literature, memorizes Hamlet — all of it — and does a guest lecture at Yale. He also acts in a film, “The Fighting Marine,” and writes articles and books of his own.

Given that unusual premise, it’s easier to understand how the boxer, James Joseph “Gene” Tunney, also forged an enduring personal friendship with George Bernard Shaw, the Irish playwright and literary giant of his time.

But as Tunney’s son, Jay R. Tunney, makes clear in “The Prizefighter and the Playwright,” these two elegant, erudite gentlemen, 41 years apart in age, had more in common than a love of letters and well-tailored tweed suits.

By the time they first met in London in 1928 — soon after Tunney had defeated the great Jack Dempsey for the second time — Tunney already was hanging out with Jazz Age literary lions such as F. Scott Fitzgerald and Thornton Wilder, and sparring playfully with Ernest Hemingway.

Across the pond, the title character in “Cashel Byron’s Profession” in some ways eerily presaged the future champ.

The playwright also followed the professional sport from afar, and since 1924 had recognized Tunney as the kind of quick, smart, “scientific” fighter who, he thought, might be able to dethrone a relentless slugger like Dempsey.

While building an amazing career record of only one loss in 87 fights, Tunney was disparaged in the sports press as a man who “read books,” a prejudice reflected in the refusal of many fans to embrace Tunney — even booing him as he accepted the championship laurel after his historic upset of Dempsey in 1926.

There is plenty of room for a book about the Shaw-Tunney connection; the boxer is rarely mentioned in Shaw biographies, and Tunney, a private man with a special aversion to dealing with the press, never said or wrote much about it for public consumption.

To fill this long-empty gap, Jay Tunney delivers a 267-page text that is straightforward, graphic, occasionally eloquent and, as a family narrative, at times almost excruciatingly personal.

While he never met Shaw, who died in 1950 at 94, Jay Tunney says researching the book gave him a deeper understanding of what the Irish bard’s relationship with his father was about.

“I began to appreciate that Shaw was much more than a friend but was mentor, priest and, as my mother always said, his spiritual father and the father he never had,” he writes.

Gene and his wife, Polly, named a daughter Joan, after the heroine of Shaw’s masterpiece, “Saint Joan”; the Shaws and Tunneys vacationed together in Brioni on the Adriatic coast; and the two men talked endlessly about literature, music, art and life. “He was the teacher, I was the pupil,” Tunney said.

Apart from the rich details of that relationship, the author offers some fascinating glimpses into Tunney’s boxing years.

In one memorable episode, a reporter sent by The Associated Press to Tunney’s training camp with instructions to find something new and “give it a feature touch” encounters the fighter in a small, book-filled hut in the woods and asks, “What are you reading?” “The Way of All Flesh,” says Tunney, instantly willing to talk to a reporter who asks about something other than boxing.

The resulting AP story, says the author, helped to explain the “enigmatic” Tunney, but also led to public ridicule of a man who, another writer said, hoped to defeat Dempsey “on a diet of classical authors.”

As a boxer, Tunney was at his best against Dempsey. Author Tunney is at his best in recounting the fabled rematch in Chicago in 1927 — the second “Battle of the Century,” in front of 120,000 fans and a worldwide radio audience.

As in their first fight, Tunney won every round — until the seventh, when he was suddenly floored by two vicious left hooks and sat groggily on the canvas, the first time he’d ever been knocked off his feet. ” … a gigantic howl of pure adrenaline careened across the darkened stadium, sounding like freight trains in the night,” the author writes.

As the world watched and listened, Dempsey ignored the referee’s order to go to a neutral corner, which delayed the start of the count and gave Tunney an extra 5 seconds to gather himself and get back on his feet at the count of nine. As Dempsey then bore in for the kill, Tunney rocked him with a breath-sapping blow to the chest, and eventually won the fight, preserving his heavyweight title.

Due to the famous “long count,” the outcome remains controversial to this day, but not to Shaw, who later wrote, “I never saw anything so wonderful as Tunney’s dance around the ring when he got up … with Dempsey rushing after him slogging wildly until Gene suddenly stopped and countered with a biff that made poor Jack think he was going to die.”

Well-chosen photos in this book evoke the Gatsby-ish 1920s — a world of beachfront homes, limousines, cloche hats and men (Shaw and Tunney, anyway) wearing fashionable plus-fours. “But,” the author says, “Gene Tunney was no Gatsby.”