When Stanley Kubrick’s “2001: A Space Odyssey” emerged in 1968, after repeated delays (filming had begun in late 1965) and nearly doubling the original $6 million budget, it was greeted as something of a disaster. Kubrick had kept a tight lid on the project, and when MGM executives got a look in March, they were aghast. At the New York premiere, a sixth of the audience walked out. Critics described it as “somewhere between hypnotic and immensely boring” (Renata Adler) and “a thoroughly uninteresting failure” (Andrew Sarris), with Pauline Kael concurring: “monumentally unimaginative . . . trash masquerading as art.”

None of that meant a thing to the younger spectators who began lining up on opening day and continued to come back. By the time I belatedly caught up with “2001” some months after its opening, acquaintances had already favored me with elaborate exegeses—metaphysical, prophetic, psychedelic—of what seemed to them not so much a film as an unbroken flow of revelation. Yet although ensconced as a canonical milestone and cited as a formative influence by filmmakers who followed, “2001” remains singular even in Kubrick’s oeuvre: slow, elliptical, deliberately enigmatic, often wordless. Its most emotionally expressive character is a dysfunctional computer, its culminating episode a sustained burst of abstraction. It is doubtful whether such a film could gather a mass audience now, and even more unlikely that any filmmaker would get the chance to risk it.

Kubrick’s risk-taking is the through-line of Michael Benson’s “Space Odyssey,” an omnivorously curious account of how the movie came to be, starting with Kubrick’s letter to the novelist and scientist Arthur C. Clarke about “the possibility of doing the proverbial ‘really good’ science fiction movie.” Mr. Benson, himself a filmmaker and artist whose projects have often been concerned with cosmological science, has put together an enlightening and entertaining narrative rich in both pointed anecdotes and lucid technical expositions. The book’s large cast of characters reflects the scale of a production so complex it seems a wonder it didn’t take even longer to complete—especially with the director still working out basic plot concepts and contemplating radically different endings almost until the wrap.

Kubrick has been mythologized as the ultimate control freak, and the obsessiveness of his concentration is self-evident, but Mr. Benson emphasizes his capacity to improvise, to respond creatively to other people’s hints, and to make large gambles. “We never had a finished script,” production designer Tony Masters recalled. “We’d get together with Stanley in the evening and talk about what we were going to do the next day—and as a result, the whole thing would change. The production department was suicidal.”

Mr. Masters was only one of a small army of recruits making crucial contributions. As Kubrick seized advantage of the ample means his earlier successes had earned him, “a big-budget Hollywood production,” in Mr. Benson’s words, “had been transformed into a giant research and development think tank.” If “2001” now seems a relic of an already unimaginable era, it is because every element of its analog simulation of a future digital age had to be imagined, invented and built by hand. Arguments over who did the imagining and inventing of any given element have simmered over the years, but Mr. Benson shows how widely diffused the creative energies were, with artisans devoting months or years to solving minute technical problems while often having scant idea of the film’s overall structure. To watch the film after reading Mr. Benson’s book is to see it as an assemblage of disparate pieces, and to marvel again at the enduring beauty of their assembling.