This is the first book on a hot topic in the field of control of nonlinear systems. It ranges from mathematical system theory to practical industrial control applications and addresses two fundamental questions in Systems and Control: how to plan the motion of a system and track the corresponding trajectory in presence of perturbations. It emphasizes on structural aspects and in particular on a class of systems called differentially flat. Part 1 discusses the mathematical theory and part 2 outlines applications of this method in the fields of electric drives (DC motors and linear synchronous motors), magnetic bearings, automotive equipments, cranes, and automatic flight control systems. The author offers web-based videos illustrating some dynamical aspects and case studies in simulation (Scilab and Matlab).