Last centurys research on sleep may be divided into two different time periods. The first half of the century was dominated by the work of Henri Piron and Nathaniel Kleitman, and was devoted to sleep experiments of a classical nature that were performed on animals and humans (Gottesmann, Nova 2013). At the beginning of the second half of the century, a major discovery identified a sleep phase during which eye movements can be recorded and dreaming occurs. William C. Dement and Michel Jouvet, dominated the next fifty years independently with their discovery of nearly all the properties concerning rapid eye movement (REM) sleep, also called paradoxical sleep. This book analyses the first major findings that were made possible by all the available methods (behavioral observations, electrophysiology, surgical interventions, pharmacology) used by both authors to characterize this sleep stage. All the successive papers by Dement and Jouvet are analyzed in turn for the period from 1955 to 1970. The results that came of the authors research environment are taken into account, and all the data available in the past and present are discussed and integrated into those findings.