The aim of this book is to o?er a self-consistent overview of a series of - sues relating entropy, information and dynamics in classical and quantum physics. My personal point of view regarding these matters is the result of what I had the good fortune to learn in the course of the years from various scientists: Heide Narnhofer in the ?rst place, who introduced me to qu- tum dynamical entropies and was a precious guide ever since, then Robert Alicki, Mark Fannes, Giancarlo Ghirardi, Andreas Knauf, John Lewis, - o?rey Sewell, Franco Strocchi, Walter Thirring, Armin Uhlmann. To me, all of them have been a constant example of rigorous mathematics and physical intuition jointly at work. Last but not least, my deep gratitude goes to my family and to the many friends on whom I could always count for support and encouragement with a special thought for Traude and Wolfgang Georgiades.