Graduate students wishing to become familiar with advanced computational strategies in classical and quantum dynamics will find in the one source both the fundamentals of a standard course as well as a detailed treatment of the time-dependent oscillator, Chern-Simons mechanics, the Maslov anomaly and the Berry phase, illustrated by many worked examples throughout the text. This second edition has been enlarged with a new chapter on topological phases in planar electrodynamics, and a discussion of the Aharonov-Bohm effect.