This book is a quantitative exposition of our current understanding of the dynamics of plant and animal populations, with the goal that readers will be able to understand, and participate in the management of populations in the wild. The book uses mathematical models to establish the basic principles of population behaviour. It begins with a philosophical approach to mathematical models of populations. It then progresses from a description of models with a single variable, abundance, to models that describe changes in the abundance of individuals at each age, then similar models that describe populations in terms of the abundance over size, life stage, and space. The book assumes a knowledge of basic calculus, but explains more advanced mathematical concepts such as partial derivatives, matrices, and random signals, as it makes use of them. The book explains the basis of the principles underlying important population processes, such as the mechanism that allow populations to persist, rather than go extinct, the way in which populations respond to variable environments, and the origin of population cycles.The next two chapters focus on application of the principles of population dynamics to manage for the prevention of extinction, as well as the management of fisheries for sustainable, high yields. The final chapter recapitulates how different population behaviors arise in situations with different levels of density dependence and replacement (the potential lifetime reproduction per individual), and how variability arises at different time scales set by a species’ life history.