This third edition text provides expanded material on the restricted three body problem and celestial mechanics.  With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications.   The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities.  The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike.   Reviews of the second edition: 'The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body