A 1977 Nobel Prize in chemistry established Russian-born, Belgium-educated scientist/philosopher Prigogine on the intellectual map. The volume at hand finally presents his ideas to a wide, English-speaking audience. (A 1979 French work, La Nouvelle Alliance, serves as the book's core.) Popularizers have already conveyed a sense of some of those ideas--such as ""closed"" and ""open"" systems in nature. Closed systems, the ideal of Newtonian mechanics, are discrete objects whose behavior is determined by a set of initial conditions and established ""laws."" The 19th century introduced the second law of thermodynamics which postulated that the expenditure of energy inevitably led to some dissipation in the form of heat. The result was an increase in entropy and disorder. Open systems maintain an exchange with the environment, extracting energy and creating order; living organisms and social systems are prototypical. Relativity theory, quantum physics, and Heisenberg uncertainty dethroned the Newtonian world view, introducing chance and probability factors. Prigogine adds the irreversability of time. Time is no longer an irrelevant variable (Newtonian equations work equally well backwards or forwards); organic processes are quintessentially time-directed and often exhibit changes of state characterized by increasing complexity (e.g., human evolution). Prigogine and his coauthor, a former co-worker in Brussels (Prigogine also teaches at the U. of Texas, Austin), set forth these ideas in the context of the history of science over the past 300 years. The result is surprisingly intense: a sort of existential drama played out against a changing cultural scene--from the rise of factories, in the wake of a Newtonian clockwork universe, to the present evidence of feedback, instability, perturbations, and chance at work in complex systems. The ultimate aim is to prove that under certain ""far-from-equilibrium"" states, a system may become self-organizing--thus achieving order out of chaos. Not all will be convinced: determinism and its modern variants offer alternative theories. But Prigogine's feat of intellectual daring is exhilarating, and the historical analyses dazzle. No one concerned with philosophy and science and their role in the modern world will want to pass it up.