As an earlier reviewer said this book provides a solution to three of the most important problems in science: 1. time's arrow 2. the measurement problem in QM 3. The existence of freewill (and the the death of the absolute determinism of Newton and Einstein). Although the book is short, I think he provided a compelling outline for the solution of all three problems. At times understanding his solutions requires understanding some advance concepts from math and physics. However, I believe an intelligent layman could skim these parts and still follow his presentation. (There is a glossary at the back of the book.)
I wish that Prigogine could have discussed in more detail the philosophical (and perhaps even religious) consequences of this work, which there are many, but few are explored and none are explored in depth. One consequence he does explore briefly is that it appears that "time precedes existence!" And at the end of the book, he also briefly addresses the worldview that emerges from his work. He says: "What is emerging is an 'intermediate' description that lies somewhere between the two alienating images of a deterministic world and an arbitrary world of pure chance. ... As we follow along the narrow path that avoids the dramatic alternatives of blind laws and arbitrary events, we discover that a large part of the concrete world around us has until now 'slipped through the meshes of the scientific net,'to use Alfred North Whitehead's expression."
I give the book my higest recommendation and hope in sequels Prigogone and his co-workers can explore the technical details (textbook level) and the philosophical consequences (layman level) of this very important and exciting work.