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

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.

1. The Action Principles in Mechanics.- 2. Application of the Action Principles.- 3. Jacobi Fields, Conjugate Points.- 4. Canonical Transformations.- 5. The Hamilton-Jacobi Equation.- 6. Action-Angle Variables.- 7. The Adiabatic Invariance of the Action Variables.- 8. Time-Independent Canonical Perturbation Theory.- 9. Canonical Perturbation Theory with Several Degrees of Freedom.- 10. Canonical Adiabatic Theory.- 11. Removal of Resonances.- 12. Superconvergent Perturbation Theory, KAM Theorem (Introduction).- 13. Poincaré Surface of Sections, Mappings.- 14. The KAM Theorem.- 15. Fundamental Principles of Quantum Mechanics.- 16. Examples for Calculating Path Integrals.- 17. Direct Evaluation of Path Integrals.- 18. Linear Oscillator with Time-Dependent Frequency.- 19. Propagators for Particles in an External Magnetic Field.- 20. Simple Applications of Propagator Functions.- 21. The WKB Approximation.- 22. Partition Function for the Harmonic Oscillator.- 23. Introduction to Homotopy Theory.- 24. Classical Chern-Simons Mechanics.- 25. Semiclassical Quantization.- 26. The "Maslov Anomaly" for the Harmonic Oscillator.- 27. Maslov Anomaly and the Morse Index Theorem.- 28. Berry's Phase.- 29. Classical Analogues to Berry's Phase.- 30. Berry Phase and Parametric Harmonic Oscillator.- 31. Topological Phases in Planar Electrodynamics.- References.