Ferdinand Verhulst's "Nonlinear Differential Equations and Dynamical Systems" is a comprehensive textbook that covers the theory and applications of nonlinear differential equations and dynamical systems. The book is divided into 15 chapters, each focusing on different aspects of the subject. It begins with an introduction to the fundamental concepts and notation, followed by a discussion of autonomous equations, critical points, and periodic solutions. The text then moves on to the theory of stability, linear equations, and methods for analyzing stability through linearisation. It also introduces perturbation theory, the Poincaré-Lindstedt method, and the method of averaging, which are essential tools for studying nonlinear systems. The book further explores relaxation oscillations, bifurcation theory, and chaos, including the Lorenz equations and fractal sets. It concludes with a chapter on Hamiltonian systems and the KAM theorem. The book includes numerous exercises, appendices, and references to support learning and research. With 127 figures, it provides visual aids to help illustrate complex concepts. The second edition is revised and expanded, offering updated information and additional material. The book is suitable for advanced undergraduate and graduate students in mathematics, physics, and engineering, as well as researchers in the field of dynamical systems. It serves as both a textbook and a reference for those interested in the analysis and understanding of nonlinear systems.Ferdinand Verhulst's "Nonlinear Differential Equations and Dynamical Systems" is a comprehensive textbook that covers the theory and applications of nonlinear differential equations and dynamical systems. The book is divided into 15 chapters, each focusing on different aspects of the subject. It begins with an introduction to the fundamental concepts and notation, followed by a discussion of autonomous equations, critical points, and periodic solutions. The text then moves on to the theory of stability, linear equations, and methods for analyzing stability through linearisation. It also introduces perturbation theory, the Poincaré-Lindstedt method, and the method of averaging, which are essential tools for studying nonlinear systems. The book further explores relaxation oscillations, bifurcation theory, and chaos, including the Lorenz equations and fractal sets. It concludes with a chapter on Hamiltonian systems and the KAM theorem. The book includes numerous exercises, appendices, and references to support learning and research. With 127 figures, it provides visual aids to help illustrate complex concepts. The second edition is revised and expanded, offering updated information and additional material. The book is suitable for advanced undergraduate and graduate students in mathematics, physics, and engineering, as well as researchers in the field of dynamical systems. It serves as both a textbook and a reference for those interested in the analysis and understanding of nonlinear systems.