This textbook provides a thorough coverage of classical mechanics. Meant for undergraduate and graduate physics students, it contains discussions on topics beneficial for researchers also. Along with standard graduate-level topics, it highlights and demonstrates the applications of classical mechanics in various areas of physics, astronomy, and astrophysics, thus emphasizing the subject's relevance to current research. Detailed explanations are provided throughout to support self-study and ensure clear understanding of concepts. The text begins with preliminary topics and then proceeds to Lagrange's equation of motion, Hamilton's principle of stationary action, and conservation principles in classical mechanics. It then extends to topics like Hamiltonian formulation of laws of mechanics, two-body central force problem, and restricted three-body problem, among others. Lagrange and Poisson brackets are discussed in exclusive chapters. The book concludes with expositions on Hamilton–Jacobi formulation of dynamics, perturbation theory in Hamiltonian mechanics, dynamics of rigid bodies, and nonlinear dynamics and chaos.