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The book aims to describe the magic world of mathematical models: starting from real-world problems, computers generate solutions based on equations. The books describes with several examples and through exercises that, if the models are well designed, they can predict how - to name just a few examples - the number of dolphins of the Aeolian islands will change as food availability and fishing activity vary; describe the blood flow in a capillary network; or calculate the PageRank of websites. This book also includes a chapter providing an elementary introduction to Octave, an open-source programming language used by the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from the site work is addressed to any student interested in knowing more on mathematical models.