This book commemorates the centenary of the birth of Georges David Birhoff, the father of the theory of Dynamical Systems. It consists of a volume of dedicated papers, reflecting the intellectual revolution of his work. This book is divided into four parts: Fundamental Paradigms — Chaos, Turbulence, Attractors, Bifurcations; Dynamical Systems and Microphysics; Self-Organization and Biological Dynamical Systems; Epistemology and History.