This book represents an attempt to give an introductory presentation of a variety of complementary methods and viewpoints that can be used in the study of a fairly broad spectrum of nonlinear dynamic systems. The skeleton of this organization consists of the three perspectives afforded by classic and some modern analytic methods, together with topological and other global viewpoints introduced by the genius of Poincaré around the turn of the century and, finally, the computational and heuristic opportunities arising from modern computers, as partially foreseen by von Neumann in 1946. On a more profound level, the interplay between computational concepts and physical theories, and what they may teach each other, has become a subject of growing interest since von Neumann's and Ulam's introduction of cellular automata.