This book presents a comprehensive treatment of classical mechanics, emphasizing mathematical methods and concepts. It covers Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics, with a focus on variational principles and analytical dynamics. The text is designed for advanced students and includes detailed discussions on topics such as oscillations, rigid body motion, and Hamiltonian formalism. The author aims to highlight the geometric and qualitative aspects of mechanical phenomena, making the book more aligned with theoretical physics courses than traditional mathematical mechanics courses. The book constructs the mathematical apparatus of classical mechanics from the beginning, requiring only standard knowledge in analysis, geometry, and linear algebra. It explores various mathematical theories that originated from mechanics, including differential equations, smooth mappings, manifolds, Lie groups, symplectic geometry, and ergodic theory. These theories have since developed into independent mathematical disciplines. The text is heavily focused on variational principles and analytical dynamics, which are fundamental to classical mechanics. The Hamiltonian formalism, in particular, has become a cornerstone of quantum mechanics and is widely used in physics. The book also discusses the significance of symplectic structures and Huygens' principle in optimization problems and engineering calculations. The appendices explore connections between classical mechanics and other areas of mathematics and physics, including Riemannian geometry, fluid dynamics, Kolmogorov's theory of perturbations, short-wave asymptotics, and the classification of caustics. These appendices are intended for advanced readers and are not part of the main course. The book was originally based on a course given by the author to mathematics students at Moscow State University. The author is grateful to various colleagues and students for their contributions to the development of the text. The translators also acknowledge the help of Dr. R. Barrar in reviewing the proofs.This book presents a comprehensive treatment of classical mechanics, emphasizing mathematical methods and concepts. It covers Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics, with a focus on variational principles and analytical dynamics. The text is designed for advanced students and includes detailed discussions on topics such as oscillations, rigid body motion, and Hamiltonian formalism. The author aims to highlight the geometric and qualitative aspects of mechanical phenomena, making the book more aligned with theoretical physics courses than traditional mathematical mechanics courses. The book constructs the mathematical apparatus of classical mechanics from the beginning, requiring only standard knowledge in analysis, geometry, and linear algebra. It explores various mathematical theories that originated from mechanics, including differential equations, smooth mappings, manifolds, Lie groups, symplectic geometry, and ergodic theory. These theories have since developed into independent mathematical disciplines. The text is heavily focused on variational principles and analytical dynamics, which are fundamental to classical mechanics. The Hamiltonian formalism, in particular, has become a cornerstone of quantum mechanics and is widely used in physics. The book also discusses the significance of symplectic structures and Huygens' principle in optimization problems and engineering calculations. The appendices explore connections between classical mechanics and other areas of mathematics and physics, including Riemannian geometry, fluid dynamics, Kolmogorov's theory of perturbations, short-wave asymptotics, and the classification of caustics. These appendices are intended for advanced readers and are not part of the main course. The book was originally based on a course given by the author to mathematics students at Moscow State University. The author is grateful to various colleagues and students for their contributions to the development of the text. The translators also acknowledge the help of Dr. R. Barrar in reviewing the proofs.