Introduction to the Perturbation Theory of Hamiltonian Systems Hamiltonian Equations to the KAM Theory Splitting of Asymptotic Manifolds The Separatrix Map Width of the Stochastic Layer The Continuous Averaging Method The Anti Integrable Limit Hill’s Formula. This book presents the basic methods of regular perturbation theory of Hamiltonian systems including KAM theory splitting of asymptotic manifolds the separatrix map averaging anti integrable limit etc. in a readable way. Although concise it discusses all main aspects of the basic modern theory of perturbed Hamiltonian systems and most results are given with complete proofs. It will be a valuable reference for Hamiltonian systems and of special interest to researchers and graduate students of the KAM community.