Philip Norman’s “Shout!: The Beatles in Their Generation” (1981), his important early biography of the band, was embraced by John Lennon’s fans but less so by Paul McCartney’s. Mr. Norman took the side of the rebellious Beatle, not the tuneful and adorable one. Mr. McCartney was said to loathe the book, and to enjoy mispronouncing its title as a barnyard epithet.

Thirty-five years later, as if to make amends, here is Mr. Norman with “Paul McCartney: The Life.” It’s an enormous and sympathetic book, written with Mr. McCartney’s tacit approval. A companion of sorts to Mr. Norman’s “John Lennon: The Life” (2008), it lays out Mr. McCartney’s more than 70 years in granular fashion while advancing a series of arguments as if they were chess pieces — notably that Mr. McCartney, as a Beatle, was as intellectual and avant-garde as he was extroverted and sweet-sounding.

Together Lennon and McCartney were among the greatest songwriters and most important cultural figures of the 20th century. Alone, the author suggests, Mr. McCartney has been “underestimated by history.” (Not by all of us, one is tempted to reply, while cuing up the “Abbey Road” medley and “Penny Lane” on Spotify.)

Is this book necessary? There are many biographies of Mr. McCartney, from Barry Miles’s authorized “Paul McCartney: Many Years From Now” (1997) to more recent ones by Peter A. Carlin and Howard Sounes.