The notion of irreversibility in physical systems has occupied the time of countless researchers for nearly 130 years. This book, written by one of the major contributors to nonequilibrium statistical physics from the Brussels group, is somewhat out of date now but nevertheless could still motivate modern developments. One will find a detailed account of what was emphasized by the Brussels group at the time of publication, and some of the contributions of the late Ilya Prigogine, who passed on in May of this year. I had the privelege of doing my graduate work in Prigogine's department at the University of Texas at Austin. This book was used heavily there, and so it brings back fond memories.