This volume compiles three series of lectures on applications of the theory of Hamiltonian systems‎,‎ contributed by some of the specialists in the field‎.‎ The aim is to describe the state of the art for some interesting problems‎,‎ such as the Hamiltonian theory for infinite‎-dimensional Hamiltonian systems‎,‎ including KAM theory‎,‎ the recent extensions of the theory of adiabatic invariants‎,‎ and the phenomena related to stability over exponentially long times of Nekhoroshev‎'‎s theory‎.‎ The books may serve as an excellent basis for young researchers‎,‎ who will find here a complete and accurate exposition of recent original results and many hints for further investigation‎.‎