A Course of Applied Mathematics for Engineers and Physicists attempts a synthesis between the various theoretical concepts with the tools and techniques useful to the engineer, aiming at an equilibrium between mathematical rigour and a practical point of view with applications in mind. THE MAIN TOPICS DISCUSSED ARE: Linear and non linear Algebra Topology (Topological and Metric spaces, Convexity Connexity, Orthogonal Projection in Hilbert spaces, etc.) Integration (Lebesgue Integral, Analytic functions, Fourier and Laplace Transforms, Distributions) The focus is on the applications of the above in Linear and Nonlinear Optimization, Combinatorial Optimization (Graphs), Dynamical Programming, Approximations, Solutions of Integral and Differential equations.