Peter Guralnick, Last Train to Memphis: The Rise of Elvis Presley (1995)
This first volume explores Elvis' youth, up until age 24, when he is inducted into the army. Guralnick is a respected cultural historian, and this two-volume work is the definitive Elvis biography.
Peter Guralnick, Careless Love: The Unmaking of Elvis Presley (2000)
This second volume picks up where Last Train to Memphis leaves off, and follows Presley through his death in 1977. Again, this two-volume work is the definitive biography.
Priscilla Presley, Elvis and Me (1986)
If you're interested more in the "inside" story from a person with a unique attachment to Presley, you might like this older book from his young bride.