This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines and in particular from Economics and Social Sciences. The first part develops the fundamental aspects of mathematical modeling, dealing with both continuous time systems (differential equations) and discrete time systems (difference equations). Particular attention is devoted to equilibria, their classification in the linear case, and their stability. An effort has been made to convey intuition and emphasize connections and concrete aspects, without giving up the necessary theoretical tools. The second part introduces the basic concepts and techniques of Dynamic Optimization, covering the first elements of Calculus of Variations, the variational formulation of the most common problems in deterministic Optimal Control, both in continuous and discrete versions.