This work is an introduction in the classical theory of calculus of variations and the theory of control of differential equations. The purpose of the book is to present classic theory, to describe the geometric and analytic setting of the problems, to study the specific mathematical methods and the underlying Hamiltonian formalism corresponding to both branches, as well to discuss all these facts in concrete situations. It is addressed especially to the students in mathematics and physics but may be useful to anybody wishing a relatively rapid introduction in the various branches and directions of study of the field.