The goal of this book is to provide a short and concise introduction to "experimental mathematics" using discrete dynamical systems as a background and Python as a tool for experimentation. Examples from diverse application areas are used throughout the book. What the author aims to accomplish is to give the reader, with the help of computer experiments, a glimpse of the richness of dynamical systems theory and various related topics, without assuming much background knowledge. Only basic calculus, some elementary linear algebra, and a bit of introductory probability theory are needed. Some familiarity with programming in Python is assumed; however, to make the book as self-contained as possible, a brief Python tutorial is included in the Appendix. Each chapter contains a number of exercises, including some more extensive projects. All programs used in the book are available online.