Theoretical study: Sets and Functions. Metric spaces (metric, topology, metric spaces, completenessof metric spaces). Topological spaces (definition of topological space, the classification of points in a topological spaces, mapping, separation axioms, subbases and bases, the convergence of sequences, limit and continuity of functions, Cartesian product, connectedness) . Normed spaces, L (X, Y) spaces.Hilbertovi spaces, Fourier analysis of Hilbert spaces.Practical classes (exercise): the exercises are performed with appropriate examples of theory that practicing a given material and therefore contribute to the understanding and practice of a given material.