This is an obligatory course for first year students. It is taught 6 hours per week. It covers the introduction of coordinates in Geometry, algebra of vectors, the classical theorems of Geometry (Menelaus, Pappus, Ceva, Desargues), inner product, exterior product, mixed triple product, lines, planes, parallelism and orthogonality, areas, volumes, conic sections and the basic theorems (Dedenlin, Apollodorus), ending with a complete study of the second order equation.