On Nov. 18, 1941, a struggling Manhattan author wrote to a young woman in Toronto to tell her to look for a new piece of his in a coming issue of The New Yorker. This short story, he said, about “a prep school kid on his Christmas vacation,” had inspired his editor to ask for an entire series on the character, but the author himself was having misgivings. “I’ll try a couple more, anyway,” he wrote, “and if I begin to miss my mark I’ll quit.”

He ended the letter by asking for her reaction to “the first Holden story,” which he said was called “Slight Rebellion Off Madison,” and signing, simply, “Jerry S.”

The writer was J. D. Salinger, then just 22, with works like “The Catcher in the Rye” still ahead of him and his literary success hardly assured. When Salinger died in seclusion in 2010, at the age of 91, he remained a mystery to his millions of readers, having shared little of himself with the world beyond the few fictional works he had published....