The volume provides and elementary introduction of the mathematical modelling in those areas on Dynamical Systems and Control Theory that arise frequently in Economics. The book is divided in two parts. In the first part the fundamental aspects of mathematical modelling are developed, 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 concrete aspects, without omitting the necessary theoretical tools. In the second part the basic concepts and techniques of Dynamic Optimization are introduced, covering the first elements of Calculus of Variations, the variational formulation of the most common problems in deterministic Optimal Control, with a brief introduction to Dynamic Programming, both in continuous and discrete versions. 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.