The focus is on the formulation and solution of mathematical models with the idea of a population employed mainly as a pedogogical tool. If the biological setting is stripped away, the material can be interpreted as topics or the qualitative behavior of differential and difference equations. The first group of models investigate the dynamics of a single species, with particular interest in the consequences of treating time and population size in discrete and continuous terms. The second group study is the interaction of two or more species. A final section on complexity and stability attempts to summarize one of the basic questions in ecology using many of the developed ideas. At the conclusion of each topic, problems are provided to provide practice with mathematical concepts and techniques and an annotated list of references is also given at these points in the material. The document concludes with solutions to problems. (MP)