Bob Dylan’s “Bringing It All Back Home,” 50 years old on Sunday, has as strong a claim as any album of its day to be called the spark that ignited the music of the 1960s. The decade was, of course, almost half over when Columbia Records released it on March 22, 1965. But just as miasmic paranoia about government did not become the general mood until after the assassinations of President John F. Kennedy and Lee Harvey Oswald in November 1963, so lyrics with jagged edges, enigmatic visions of America adrift accompanied by dark, cynical laughter, were not common until Mr. Dylan’s surrealist poetry entered the mainstream of popular song.

One need only listen to the Beatles as the boyishness of “A Hard Day’s Night” gave way to the self-doubt of “Help!” and the inward gazing of ”Rubber Soul” to hear that pop music’s leading composers suddenly grew up between 1964 and 1966. Teen obsessions with love and jealousy were replaced by a deeper awareness of life’s existential problems.

Credit for this new lyrical complexity is usually given to Mr. Dylan, with “Bringing It All Back Home” being the fullest expression of the artistic freedom he won for his fellow troubadours.

The album has a split personality, as if conceived for a dual purpose: to expand the minds of young pop music fans and to shatter Mr. Dylan’s reputation as pied piper for his generation.

Side one took an electric knife to his image as an earnest folkie. “Subterranean Homesick Blues,” “Maggie’s Farm” and “Outlaw Blues” have a driving R&B momentum and swagger. He plays an amplified guitar and is backed by several more of them. This crackling sound, when he brought it on stage with a top-notch band during the 1965 Newport Folk Festival, was so poorly received by many in his former constituency that he didn’t return to the festival for 37 years.

None of his lyrics on the album were overtly political, as his antiwar anthems “Blowin’ in the Wind” and “Masters of War” had been. By now the snarling tone of his voice was enough to convey his attitude toward all authority. A line from the first track, “Subterranean Homesick Blues,” inspired the name of the Weather Underground, the hardline New Left revolutionaries: “You don’t need a weatherman / To know which way the wind blows.”

In fact, the album marked his public disenchantment with organized protests and a stronger identification with loner misfits. By the end of 1965 he had stopped performing with his girlfriend and supporter Joan Baez; their friendship wasn’t repaired until 1975. “Don’t ask me nothin’ about nothin’ / I just might tell you the truth,” he warns in “Outlaw Blues.”

Other songs on the album have other functions. “Bob Dylan’s 115th Dream” reimagines the founding of America as led by a “Captain Arab” and a rollicking crew of buccaneers, one of whom tells the absurdist tale. “Captain Arab he started / Writing up some deeds / He said, ‘Let’s set up a fort / And start buying the place with beads.’”

On the recording, the song starts and then abruptly stops after the first line; Mr. Dylan is laughing too hard to go on. The inclusion of this flawed first take dispels the illusion that for him music is ever perfected. Like his dreams, the completed version of the song is one of hundreds of other possible ones.

Side two is mainly acoustic, but spookily so. “It’s Alright, Ma (I’m Only Bleeding)” and “Gates of Eden” are doom-laden, as if the singer were free associating through a Salvador Dalí landscape. The album also includes two of the loveliest ballads Mr. Dylan ever wrote. “It’s All Over Now, Baby Blue” is a new kind of break-up song (“You must leave now, take what you need, you think will last / But whatever you wish to keep, you better grab it fast”); while “Love Minus Zero/No Limit” has some of his most quoted lines: “My love she speaks softly / She knows there’s no success like failure / and that failure’s no success at all.”

The album also yielded Mr. Dylan’s first No. 1 radio hit. “Mr. Tambourine Man,” the first cut on side two, was covered by the Byrds and released in April 1965 in a guitar-rich, densely harmonized arrangement often cited as the beginning of folk rock. As Mr. Dylan was the composer but not the voice, he benefited from its commercial success but wasn’t tainted by charges of selling out—a trick he has managed throughout his career.

The photograph by Daniel Kramer on the jacket of “Bringing It All Back Home” is loaded with clues about the clashing influences Mr. Dylan was absorbing. The scruffy kid visible on earlier covers is now a coiffed sophisticate. Albums by Lotte Lenya, Robert Johnson and the Impressions, as well as a copy of his own “Another Side of Bob Dylan,” are placed literally behind him.

He strokes a gray cat while holding a movie magazine on his lap. An elegant woman in a red dress leans back on a couch. A copy of Time (President Lyndon Johnson on the cover) is at her elbow, just above a yellow Fallout Shelter sign.

The voyeuristic style of the photograph, distorted at the edges as though seen in an altered state, is another clue. According to his biographers, he began to experiment with LSD in the spring of 1964 and turned the Beatles on to marijuana during their U.S. visit later that year.

“Bringing It Back Home” rose to No. 6 on the Billboard charts, the first Dylan album to break into the Top 10. It was hailed by rock critics then and has never fallen out of favor. In the latest Rolling Stone poll it ranks 31 on the list of “500 Greatest Albums of All Time.” In its fast-paced rhymes and knowing American slang, it looks back to the patter songs of Dorothy Fields and forward to the exuberance of rap.

Despite such acclaim, Mr. Dylan has not forgotten those he thinks slighted him in the ’60s. In a rambling speech last month, he singled out not only critics who hadn’t liked his voice (“sound like a frog”), but the songwriters Jerry Leiber and Mike Stoller, who hadn’t liked his music (“they weren’t saying anything serious”).

Mr. Dylan is often held responsible for killing Tin Pan Alley. His songs commonly stripped out the “B” section of the 32-bar popular song in favor of repeated “A” sections, as in the 12-bar blues. It’s therefore odd—or perhaps for him typically perverse—that his new record, “Shadows in the Night,” is a return to standards (in AABA form) sung by Frank Sinatra and Nat King Cole.

“Bob freed your mind the way Elvis freed your body,” as Bruce Springsteen has famously said. Three months after “Bringing It All Back Home,” Columbia released the even more caustic “Highway 61 Revisited,” and nine months after came “Blonde on Blonde”—a streak of creativity few other songwriters have matched, not even Mr. Dylan.