Synchronization : from simple to complex Part I: General mechanisms of synchronization General remarks Forced synchronization of periodic oscillations Mutual synchronization of periodic oscillations Homoclinic mechanism of synchronization of periodic oscillations n:m synchronization of periodic oscillations Forced synchronization of periodic oscillations in the presence of noise Chaos synchronization Synchronization of noise induced oscillations Conclusions to Part I Part II: Case studies in synchronization Synchronization of anisochronous oscillators Phase multistability Synchronization in systems with complex multimode dynamics Synchronization of systems with resource mediated coupling Conclusions to Part II