Camilo Enrique Argoty from the Sergio Arboleda University in Bogota, Colombia visits Institute for Research in Fundamental Sciences in Tehran, Iran between May 4 and May 12, 2016 for giving some lectures on the model theory of Hilbert spaces. This mini course gives a panorama of model theory of Hilbert spaces in two frameworks: continuous first order logic and abstract elementary classes. The program of the sessions is as follows:

**First session:**Basic Hilbert space Model Theoretic Properties: Categoricity, stability, characterization of types, quantifier elimination, characterization of non-forking

**Second session:**Hilbert spaces with a normal operator: Elementary equivalence, $\aleph_0$ categoricity up to perturbations, types as spectral measures, quantifier elimination, non-forking, orthogonality and domination.

**Third session:**Hilbert spaces with a closed unbounded self-

adjoint operator: Metric abstract elementary classes (MAEC’s); a

for a Hilbert space with a closed unbounded self-adjoint operator; continuous first order elementary equivalence; types as spectral measures; non-forking, orthogonality and domination.

**Fourth session:**Model theory of representations of C*-algebras: Elementary equivalence; $\aleph_0$ categoricity up to perturbations; the generic representation of a C*-algebra; homoeomorphism of the stone space and quasi-state space and quantifier elimination; Non-forking, orthogonality and domination.

**Fifth session:**Further work: Elementary equivalence in *-representations of *-algebras