The main aim of this course is the study, in some depth, of subjects that come from any area of Mathematical Analysis and Set Theory. These subjects can be chosen after discussion with the students. The basic characteristic of this course is the active participation of students via presentations. Some subjects of the course can be the following: Analytic number theory, infinite combinatorial, combinatorial, Harmonic analysis, Harmonic analysis in locally compact abelian groups, General topology, Geometrical measure theory, Measure theory, Convex geometrical analysis, History of mathematical analysis, Theory of real functions, Set theory, Operator theory, Calculus of variations, Partial differential equations, Complex analysis, Probability methods in combinatorial, Integral transformations, Functional analysis, Spectral theory.