Here is a text that presents classical dynamics from a modern geometrical viewpoint, uniting this new perspective with the totality of knowledge in the field and introducing mathematical techniques gradually as the reader studies the standard topics. The
concepts of differential geometry are developed as a calculation tool, with emphasis on applications and not rigor. While Dynamics treats traditional topics in a general way, it frequently adds a nontraditional approach through the new geometrical method, for instance, recent developments in the variance of mechanical systems under perturbation and Lie algebra techniques are introduced for the first time in any textbook. Topics covered include phase flows, Lagrangian dynamics, rigid bodies,
small oscillations, invariants, Hamiltonian dynamics on the cotangent bundle, dynamics on phase space, action-angle variables, and invariant tori.