-------------------------------------------------------------------- Harold Weitzner Abstract The idea of an adiabatic invariant and its properties are introduced with the simple problem of pendulum with time varying length. It is shown how to formulate the problem as a Hamiltonian system. Non-linear systems are then treated. The motion of a charged particle in given electromagnetic fields is then described and the standard theory of adiabatic invariants for the system is given. Finally, it is shown that the standard theory may be extended in surprising ways to give a broader range of applicability. One particular example treated was done in collaboration with Jonathan Keyes. The use of adiabatic invariants is briefly described. -----------------------------------------------------------------------