The study of the interstellar medium is certainly one of the most recently developed astrophysical topics. Indeed, to understand the physical status of this medium, one should observe it at every wavelength, especially in radio and in the ranges which are only accessible from space such as Infra Red, X and gammas. Thanks to many new observations we now know that interstellar gas is quite inhomogeneous, since it is made from relatively cold and dense phases (interstellar clouds), surrounded by a relatively hot and tenuous medium. The summer school which took place from September 1 to 16 at the Institut d'Etudes Scientifiques of Cargese, and from which this book originates, was devoted to the analysis of this second diffuse, hot and tenuous component. The eleven sets of lectures which were presented at this school constitute the chapters of this book. They review different aspects (observations, determination of the physical properties and evolution) of this diffuse medium. In the first chapter, J. Lequeux (Marseille Observatory) introduces the study of the diffuse interstellar medium which plays a major role in galactic evolution. His contribution provides some historical references on this subject, such as a copious bibliography on the analysis and observations of the interstellar medium.