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This book is an introduction to mathematical biology for students with no experience in biology, but who have some mathematical background. The work starts from population dynamics and ecology, following a tradition that goes back to Lotka and Volterra, and use it as the area where to understand different types of mathematical modeling, and the idea of qualitative agreement with data. Shorter sections are devoted to infectious diseases, to molecular networks, and finally to excitable media. The book also includes a collections of problems designed to approach more advanced questions. This material has been used in the courses at the University of Trento, directed at students in their fourth year of studies in Mathematics. It can also be used as a reference as we provide up-to-date developments in several areas.