The theory of nonlinear, complex systems has become by now a proven problem-solving approach in the natural sciences. And it is now also recognized that many if not most of our social, ecological, economical and political problems are essentially of a global, complex and nonlinear nature. And it is now further accepted than any holistic perspective of the human mind and brain can hardly be achieved by any other approach. In this wide-ranging, scholarly but very concise treatment, physicist, computer scientist and philosopher Klaus Mainzer discusses, in essentially nontechnical language, the common framework behind these ideas and challenges. Emphasis is given to the evolution of new structures in natural and cultural systems and we are lead to see clearly how the new integrative approach can give insights not available from traditional reductionistic methods. The fifth edition enlarges and revises almost all sections and supplements an entirely new chapter on the complexity of economic systems. From the reviews of the fourth edition:"… this highly recommended book is a wonderful resource for intuitive basic ideas in the need of rigorous formulation." (Albert A. Mullin, Zentralblatt MATH)