“Rock and roll’s been going downhill ever since Buddy Holly died,” said “John Milner,” a character in the film American Graffiti. That’s a bit of an exaggeration but it’s easy to understand why Holly fans get carried away. His “brush-and-broom” guitar style, inimitable vocals, and infectious, rockabilly-based music influenced innumerable rockers in subsequent decades.

To find out why, listen to this album, the best Holly anthology extant, which preserves such well-known gems as “Oh Boy,” a million-seller recorded in 1957 with his group the Crickets; “Peggy Sue,” Holly’s giant solo hit from the same year; “Maybe Baby” and “Think It Over,” both 1958 chart tunes for Holly and the Crickets; and “Raining in My Heart” and “It Doesn’t Matter Anymore,” two posthumous hits. Also, the beautiful “Everyday” and “True Love Ways,” the frequently covered “Rave On,” the smash rocker “That’ll Be the Day,” and much more. That Holly recorded all these fresh-sounding classics two decades ago and over a period of just a few years is amazing. It makes you wonder what he could have accomplished had he not died before his 21st birthday.