This text presents a rare mix of the latest mathematical theory and procedures in the area of nonlinear difference equations and discrete dynamical systems, together with applications of this theory to models in economics and other social sciences. The theoretical results include not only familiar topics on chaos, bifurcation stability and instability of cycles and equilibria, but also some recently published and some as yet unpublished results on these and related topics (for example, the theory of semiconjugates). In addition to rigorous mathematical analysis, the book discusses several social science models and analyzes some of them in substantial detail. This book is of potential interest to professionals and graduate students in mathematics and applied mathematics, as well as researchers in social sciences with an interest in the latest theoretical results pertaining to discrete, deterministic dynamical systems.