Polynomials, roots of polynomials, fundamental theorem of algebra, linear algebra, Gauss elimination, methods for solving systems of linear equations, linear spaces, linear dependence and independence, base, dimension, coordinates, linear mapping, matrices, matrix operations, determinant, LU decomposition, affine space, eigenvalues and eigenvectors, orthogonality, analytic geometry, linear codes. Semi groups, monoids, groups, Abelian groups, Euler-Fermat theorem, modular arithmetic, Chinese remainder theorem, primality testing. Residual class fields, polynomials over finite fields, irreducibility, rings and fields of polynomials, Euclid´s algorithm for polynomials over Zp, applications of finite fields. Boolean algebra. Binary relations and their properties, directed graphs and binary relations, equivalence and order relations, lattices and distributive lattices. Homomorphisms of structures described by operations and/or relations, free objects and free algebras.