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The lecture notes contained in this volume were presented at the AMS Short Course on Population Biology, held August 6-7, 1983, in Albany, New York in conjunction with the summer meeting of the American Mathematical Society. These notes will acquaint the reader with the mathematical ideas that pervade almost every level of thinking in population biology and provide an introduction to the many applications of mathematics in the field. Research mathematicians, college teachers of mathematics, and graduate students all should find this book of interest. Population biology is probably the oldest area in mathematical biology, but remains a constant source of new mathematical problems and the area of biology best integrated with mathematical theory. The need for mathematical approaches has never been greater, as evolutionary theory is challenged by new interpretations of the paleontological record and new discoveries at the molecular level, as world resources for feeding populations become limiting, as the problems of pollution increase, and as both animal and plant epidemiological problems receive closer scrutiny. A background of advanced calculus, introduction to ordinary and partial differential equations, and linear algebra will make the book accessible. All of the papers included have high research value. A list of the contents follows.