This is a textbook on classical Hamiltonian dynamics designed primarily for students commencing graduate studies in physics. The aim is to cover all essential topics in a relatively concise format, without sacrificing the intellectual coherence of the subject, or the conceptual precision which is the sine qua non of advanced education in physics.

Encouraged by my colleagues at New York University, I have taken it as a pedagogical challenge to create a textbook suitable for a twenty-first-century course of duration no more than one semester (at NYU, the material is covered in about two-thirds of a semester). To do so, I have chosen to limit the scope of the book in certain important ways. It is assumed that the student has already had a course in which Newtonian mechanics, in both F = ma and Lagrangian versions, has been systematically developed and applied to a standard array of soluble examples: the harmonic oscillator, the simple pendulum, the Kepler problem, small oscillations (normal modes), and rigid-body motion. In the present book, the Hamiltonian formulation in phase space is introduced at the outset and applied directly to the same familiar systems.

Topics usually found in more encyclopedic textbooks, but omitted from the present treatment, include dissipative systems, nonholonomic constraints, special and general theories of relativity, continuum mechanics, and classical field theory. A further choice I have made is to limit the use of advanced differential geometry.