The main intention and objective of the Samos Conference on 'Singular Behavior and Nonlinear Dynamics' held on 18-26 August 1988 was to bring together a meeting of nonlinear scientists. This is volume 1 of the proceedings containing the theoretical papers. A wide diversity of viewpoints, trends and schools of thought, useful exchange of ideas were presented. There were several review articles and many research papers with recent results. The more applied papers are in Volume II.