The Euler-Lagrange equation. First integrals. Geodesics. Minimal surface of revolution. Several dependent variables. Isoperimetric problems. Fermat’s principle. Dynamics of particles. The vibrating string. The Sturm-Liouville problem. The vibrating membrane. Theory of elasticity. Quantum mechanics. The principles of Feynman and Schwinger in Quantum mechanics. Variational principles in hydrodynamics.