Many nonlinear systems exhibit complex and counter-intuitive dynamics that contrast with their simplicity, requiring advanced concepts often absent from basic science education. This textbook, developed from graduate courses taught by the authors, offers a richly illustrated introduction to nonlinear dynamical systems and chaos, providing a solid foundation for this captivating subject. It caters to both newcomers, including undergraduates, and those seeking a concise overview of essential concepts for nonlinear scientists. The first two chapters outline the fundamental concepts necessary for describing nonlinear dynamical systems and their stability. The third chapter introduces bifurcation, highlighting changes in a system's qualitative behavior. The fourth chapter explores oscillations, from their emergence to destabilization and response to external forces. The fifth and sixth chapters address complex behaviors in higher-dimensional state spaces, focusing on quasi-periodicity and chaos, including their general properties and quantitative characterization methods. Each chapter is accompanied by exercises that range from direct applications of introduced concepts to more complex problems integrating ideas from various chapters, as well as numerical explorations.
