The book "Introduction to Mechanics and Symmetry" is a second edition of a textbook that provides a basic exposition of classical mechanical systems. It is written by Jerrold E. Marsden and Tudor S. Ratiu. The book is intended for senior undergraduate and graduate students in science and engineering, and it emphasizes concrete applications of symmetry and mechanics. The text is structured to provide a comprehensive foundation in mechanics, with a focus on geometric methods and the application of symmetry principles. The book includes a detailed introduction that serves as a guide for readers, covering topics such as Lagrangian and Hamiltonian formalisms, rigid bodies, Lie-Poisson brackets, Poisson manifolds, momentum maps, and the dynamics of incompressible fluids. It also discusses nonlinear stability, bifurcation theory, and the Poincaré-Melnikov method. The text is complemented by a solutions manual and internet supplements, which provide additional material for students and instructors. The authors are both prominent figures in the field of mechanics and mathematics. Marsden is a professor at Caltech and has made significant contributions to the study of mechanical systems with symmetry. Ratiu is a professor at the University of California, Santa Cruz and the Swiss Federal Institute of Technology. Both have extensive research experience and have been involved in various academic and research activities. The book is divided into chapters that cover a wide range of topics in mechanics, including Hamiltonian systems, infinite-dimensional systems, manifolds, vector fields, differential forms, symplectic manifolds, cotangent bundles, Lagrangian mechanics, variational principles, constraints, rotating systems, Lie groups, Poisson manifolds, momentum maps, and Lie-Poisson and Euler-Poincaré reduction. Each chapter provides a detailed explanation of the concepts, with examples and applications that illustrate the theoretical material. The book is well-structured and provides a solid foundation for further study in mechanics and symmetry. It is recommended for students and researchers interested in the application of symmetry principles in mechanical systems. The text is supported by a solutions manual and internet supplements, which enhance the learning experience and provide additional resources for students and instructors.The book "Introduction to Mechanics and Symmetry" is a second edition of a textbook that provides a basic exposition of classical mechanical systems. It is written by Jerrold E. Marsden and Tudor S. Ratiu. The book is intended for senior undergraduate and graduate students in science and engineering, and it emphasizes concrete applications of symmetry and mechanics. The text is structured to provide a comprehensive foundation in mechanics, with a focus on geometric methods and the application of symmetry principles. The book includes a detailed introduction that serves as a guide for readers, covering topics such as Lagrangian and Hamiltonian formalisms, rigid bodies, Lie-Poisson brackets, Poisson manifolds, momentum maps, and the dynamics of incompressible fluids. It also discusses nonlinear stability, bifurcation theory, and the Poincaré-Melnikov method. The text is complemented by a solutions manual and internet supplements, which provide additional material for students and instructors. The authors are both prominent figures in the field of mechanics and mathematics. Marsden is a professor at Caltech and has made significant contributions to the study of mechanical systems with symmetry. Ratiu is a professor at the University of California, Santa Cruz and the Swiss Federal Institute of Technology. Both have extensive research experience and have been involved in various academic and research activities. The book is divided into chapters that cover a wide range of topics in mechanics, including Hamiltonian systems, infinite-dimensional systems, manifolds, vector fields, differential forms, symplectic manifolds, cotangent bundles, Lagrangian mechanics, variational principles, constraints, rotating systems, Lie groups, Poisson manifolds, momentum maps, and Lie-Poisson and Euler-Poincaré reduction. Each chapter provides a detailed explanation of the concepts, with examples and applications that illustrate the theoretical material. The book is well-structured and provides a solid foundation for further study in mechanics and symmetry. It is recommended for students and researchers interested in the application of symmetry principles in mechanical systems. The text is supported by a solutions manual and internet supplements, which enhance the learning experience and provide additional resources for students and instructors.