Introduction to the perturbation theory of Hamiltonian systems 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. Despite its small size 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 of interest to researchers and graduate students of the KAM community and to scientists working in mechanics. 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. Despite its small size 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 of interest to researchers and graduate students of the KAM community and to scientists working in mechanics