Cole Porter’s story is pretty much a Cole Porter story. That much is clear in a new collection of his letters. The composer who wrote the music and lyrics for “Kiss Me, Kate,” which won the first Tony for Best Musical in 1949 — as well as for such hit songs as “Night and Day,” “Begin the Beguine,” “I Get a Kick Out of You,” “You’re the Top” and “I’ve Got You Under My Skin” — led a madcap existence with just enough tragedy to keep the rest of us from getting jealous.

Porter was born in 1891 in Peru, Ind., to a druggist father and a mother who encouraged his musical and theatrical interests. When he was 8, he recalls, his wealthy grandfather used to drive him into the Indiana countryside, rein in the horse, point to the county poorhouse with his buggy whip and, for reasons that are not quite clear, say, “That, Cole, is the place you will end up.”

As a teen, Porter attended Worcester Academy in Massachusetts and set his sights on Yale. On his first try at the Yale entrance exam, he failed the classics portion but passed algebra. When he retook the exam, he passed the classics and failed algebra. Drum roll, please! Yale let him in anyway, and he hit the ground running, writing some 300 songs there, or so he claimed, as well as his first surviving musical, “The Pot of Gold.”

A year after graduating, he found himself in New York, though his first Broadway show, “See America First,” was labeled “the worst musical comedy in town” by one critic. Porter registered for the draft in 1917 and was sent to France. His duties remain a mystery, though he seemed to have enjoyed the war, writing to his mother that “I like my job and my health was never better.”

“The Letters of Cole Porter” is an intimidating marvel of scholarship, though editors Cliff Eisen and Dominic McHugh weave his correspondence into a mostly tidy account by adding diary excerpts, newspaper clippings and plentiful commentary of their own. There are Cole Porter biographies already (as well as two biopics, nearly 60 years apart, with Cary Grant and then Kevin Kline playing the composer), and another seems unnecessary. Considering all the connective tissue, “The Letters of Cole Porter” amounts to the last word, a work as disjointed and delightful as any of Porter’s unforgettable songs.

One critic described a Porter show as having “something about it like the sack of Rome; it is like reviewing . . . a deluge of music, costumes, angels, scenery, food, vivacity and week-end charades.” But all that vivacity didn’t arise just from high spirits. Porter was a consummate student. His grasp of algebra may have been wobbly, but another critic wasn’t far wrong when he said the composer was “essentially a parodist” who could write any type of song. “Sponge” might be a better word, though, because he admitted to studying the music of Richard Rodgers, Jerome Kern and Irving Berlin and taking what he could from them.

Porter’s strong work ethic got him to the top fast and kept him there long enough to rub shoulders with everybody who was anybody in showbiz. Ethel Merman, Fred Astaire, Sophie Tucker, Jimmy Durante, Noël Coward, Katharine Hepburn: Celebs such as these appear on almost every page. Zelda and F. Scott Fitzgerald pass through, as do the Duke and Duchess of Windsor.

His is not entirely a tale of champagne and caviar, though. His marriage to Linda Lee Thomas (“the most perfect woman in the world”) didn’t stop him from taking on scores of male lovers, though he agonized over her emphysema and grieved her death. He also had physical ailments of his own after a horse threw him and caused compound fractures in both legs. At first, the injuries didn’t seem to slow him much. But a few years before his death in 1964, his right leg was amputated, and his creative life came to a halt.

Cole Porter lived long enough to see “Kiss Me, Kate” filmed in “that silly 3D.” He ultimately warmed to television, though when a musical revue of his songs aired in 1956, he insisted on overseeing every aspect of the staging. “I have been in love with every show I’ve written,” he said, “and it hurts and irritates me to hear one of my tunes mistreated.” Never one to underestimate his own achievements, the composer takes more than a little credit for helping the medium come of age. In the years BCP (Before Cole Porter), TV was “nice and folksy,” but “now she’s got class!”

It’s almost impossible to go to a cabaret these days and not hear a Cole Porter song.

His music has been performed by Ella Fitzgerald, Frank Sinatra, Judy Garland and countless jazz artists. The centenary of his birth was celebrated during the halftime show of the 1991 Orange Bowl, and that same year, his face appeared on a U.S. postage stamp. Oh, and he has a star on the Hollywood Walk of Fame.

Cole Porter overflowed with the one trait that all but guarantees artistic success: self-confidence. So he probably never believed his grandpa’s prophecy. But he sure showed the old guy, didn’t he?

David Kirby is the author of “Crossroad: Artist, Audience, and the Making of American Music.”

The Letters of Cole Porter

By Cliff Eisen and Dominic McHugh

Yale University. 672 pp. $35