This book is authored by Belgian writers, one of whom is Ilya Prigogine, a world-renowned scientist and Nobel Prize laureate, well-known to Soviet readers through many of his works translated into Russian, including the monographs "Thermodynamic Theory of Structure, Stability, and Fluctuations" (Moscow: Mir, 1973) and "Self-Organization in Non-Equilibrium Systems" (Moscow: Mir, 1979). In this accessible volume, the authors provide an overview of methods developed in recent years in the field of nonlinear dynamics for studying complex systems and processes, such as evolution and self-organization. The book includes concrete examples from various scientific disciplines, ranging from chemistry and physics to biology, sociology, and climatology. It is an essential read for students in the natural sciences and professionals across diverse fields.