Introduction.- The Action Principles in Mechanics.- The Action Principle in Classical Electrodynamics.- Application of the Action Principles.- Jacobi Fields, Conjugate Points.-Canonical Transformations.- The Hamilton-Jacobi Equation.- Action-Angle Variables.- The Adiabatic Invariance of the Action Variables.- Time-Independent Canonical Perturbation Theory .- Canonical Perturbation Theory with Several Degrees of Freedom.- Canonical Adiabatic Theory.-...