Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1 aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Written by experts, each chapter is self-contained and aims to clearly illustrate some of the mathematical theories of nonlinear systems. The book should be suitable for some graduate and postgraduate students in mathematics, the natural sciences, and engineering sciences, as well as for researchers (both pure and applied) interested in nonlinear systems. The common theme throughout the book is on solvable and integrable nonlinear systems of equations and methods/theories that can be applied to analyze those systems. Some applications are also discussed.Features: Collects contributions on recent advances in the subject of nonlinear systems Aims to make the advanced mathematical methods accessible to the non-expert in this field Written to be accessible to some graduate and postgraduate students in mathematics and applied mathematics Serves as a literature source in nonlinear systems