This book, "Mathematical Methods of Classical Mechanics" by V.I. Arnold, is part of the Graduate Texts in Mathematics series. It is translated from the Russian edition by K. Vogtmann and A. Weinstein and published by Springer Science+Business Media, LLC. The book covers the mathematical foundations of classical mechanics, including Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics. It is designed for readers with a background in standard courses in analysis, geometry, and linear algebra. The content is structured into three main parts: Newtonian Mechanics, Lagrangian Mechanics, and Hamiltonian Mechanics. Each part includes detailed chapters on various topics such as variational principles, differential forms, symplectic manifolds, canonical formalism, and perturbation theory. The book also includes several appendices that explore connections between classical mechanics and other areas of mathematics and physics, such as Riemannian geometry, fluid dynamics, and asymptotic methods. The author, V.I. Arnold, emphasizes the geometric and qualitative aspects of the phenomena discussed, making the book more accessible to theoretical physicists than to mathematicians. The book is based on lectures given by Arnold at Moscow State University and has been influenced by contributions from several colleagues and students.This book, "Mathematical Methods of Classical Mechanics" by V.I. Arnold, is part of the Graduate Texts in Mathematics series. It is translated from the Russian edition by K. Vogtmann and A. Weinstein and published by Springer Science+Business Media, LLC. The book covers the mathematical foundations of classical mechanics, including Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics. It is designed for readers with a background in standard courses in analysis, geometry, and linear algebra. The content is structured into three main parts: Newtonian Mechanics, Lagrangian Mechanics, and Hamiltonian Mechanics. Each part includes detailed chapters on various topics such as variational principles, differential forms, symplectic manifolds, canonical formalism, and perturbation theory. The book also includes several appendices that explore connections between classical mechanics and other areas of mathematics and physics, such as Riemannian geometry, fluid dynamics, and asymptotic methods. The author, V.I. Arnold, emphasizes the geometric and qualitative aspects of the phenomena discussed, making the book more accessible to theoretical physicists than to mathematicians. The book is based on lectures given by Arnold at Moscow State University and has been influenced by contributions from several colleagues and students.