This book deals with important questions of current interest in the biological sciences such as chaos, fractals, cellular automata, nonlinear dynamics, time series analysis. In addition to dealing with these modern topics, the text also shows applications of the mathematics in traditional settings with analyses of important applications of linear dynamics such as exponential growth and decay, compartmental analysis, diffusion. The book is written at an elementary level, teaching basic techniques in dynamics to an audience that is non-mathematical. The book is based on a course that has been taught to undergraduate biology students. There are a considerable number of examples derived from the experimental literature showing how the mathematical concepts can be translated into analysis of experimental data. The authors include extensive sets of exercises to teach basic mathematical concepts and their applications. There are also computer exercises that guide the student through classic computations. 1. Finite-Difference Equations -- 2. Boolean Networks and Cellular Automata -- 3. Self-Similarity and Fractal Geometry -- 4. One-Dimensional Differential Equations -- 5. Two-Dimensional Differential Equations -- 6. Time-Series Analysis.