This textbook grew out of a course that the highly respected applied mathematician Lee Segel taught at the Weizmann Institute. This book represents the unique perspective on mathematical biology of Segel and his co-author Leah Edelstein-Keshet (author of the popular SIAM book, Mathematical Models in Biology). It introduces differential equations, biological applications, and simulations, with emphasis on molecular events (biochemistry and enzyme kinetics), excitable systems (neural signals), and small protein and genetic circuits. The exposition combines clear and useful mathematical methods with plenty of applications to illustrate the power of such tools, along with many exercises in reasoning, modelling and simulation. The reader will also find suggestions for further study and appendices containing useful background material. These features make the book ideal for students at the advanced undergraduate or graduate level in both biology and mathematics who wish to experience the application of mathematical techniques to the biological sciences.