In this introductory presentation we will discuss the strong relation between Hamiltonian Dynamics and Fusion Plasma Physics. Starting from some historical remarks and basic concepts of fusion plasmas, we will present the advantages of the Hamiltonian formalism in describing magnetic field lines and charged particle orbits. We will consider integrable Hamiltonian systems describing particle motion under specific magnetic field symmetries and utilize a transformation to Action-Angle variables. The latter will be shown to allow for a systematic dynamical reduction as well as the calculation of all the orbital frequencies (Orbital Spectrum) which is the first step for the study of complex particle dynamics under the presence of perturbative symmetry-breaking modes rendering the system non-integrable. The resonant character of the modeparticle interactions suggests that the effect of the perturbations is strongly localized in the phase space. The specific resonance locations can be predicted in terms of the calculated unperturbed Orbital Spectrum. Moreover, the existence of Transport Barriers, related to non-twist conditions of the particle orbits is shown to be predicted, and confirmed by numerical orbit calculations. Hamiltonian bifurcations and chaos of particle orbits will also be discussed. The presented methods and results demonstrate the theoretical and practical advantages of the Hamiltonian formalism in terms of studying particle energy and momentum transport in fusion plasmas under the presence of multi-scale perturbations and its implications on the efficient operation of future fusion devices.