Michel Jouvet is perhaps the world's leading sleep and dream researcher. He discovered a mysterious dream state that he called paradoxical sleep. This third category of brain activity (distinct from sleeping and waking) is a state of very deep sleep with some specific motor events, including rapid eye movements (REM). In The Paradox of Sleep, Jouvet takes the reader on a scientific and sociological tour of the history of sleep and dream research, concluding with his own ideas on the function of dreaming.

Jouvet tells the story of a handful of neurobiologists, including himself, who pioneered sleep and dream research in the 1950s. He describes the technical and ideological obstacles they faced and opens his own laboratory to the reader, explaining anatomical, biochemical, and even genetic techniques. He also touches on psychological, philosophical, and metaphysical aspects of sleep and dreaming.

A key section of the book is Jouvet's discussion of why we dream. After summarizing Freud's theory of dreams, he contrasts it with current neurobiological data. Finally, he outlines his own controversial theory about why we dream: to preserve our individuality. Dreaming, claims Jouvet, is necessary for the genetic reprogramming of our brain.