This volume is the result of the authors' lectures and seminars given at Tiibingcn University and elsewhere. It represents a summary of our learning process in non-linear Hamiltonian dynamics and path integral methods in nonrelativistic quantum mechanics. While large parts of the book are based on standard material, readers will find numerous worked examples which can rarely be found in the published literature. In fact, toward the end they will find themselves in the midst of mod- em topologica

Introduction
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. Tune-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. Poincare 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 Chem-Simons Mechanics
25. Semicalssical Quantization
26. The"Maslov Anomaly and the Morse Index Theorem
27. Maslov Anomaly and the Morse Index Theorem
28. Berry's Phase
29. Classical Analoues to Berry's Phase
30. Berry Phase and Parametric Harmonic Oscillator
31. Topological Phases in Planar Electrodynamics
References
Subject Index