The two volumes of these Proceedings contain recent results and some review articles on major topics of Nonlinear Dynamical Systems: Chaos, Solitons, Bifurcations, Qualitative and Quantitative aspects of nonlinear phenomena that were presented at the International Conference of Samos. The first volume is devoted to theoretical analysis while the second contains a wealth of applied results from Solid State Physics, Fluid Mechanics, Josephson junctions, Optical Fibers and Biological systems. The major aim of the organizers was to bring together mathematicians and physicists from both the Coherent (solitonic) and Chaotic aspects of Nonlinear Dynamics as well as some more traditional theorists of Dynamical Systems.