The course covers signed measure, Hahn decomposition, measures on metric spaces, Radon-Nikodym theorem, Lebesgue decomposition, dual spaces, weak topologies, Banach-Alaoglu theorem, adjoint operators, compact operators and their spectrum, Fredholm alternative, Hilbert spaces and operators on Hilbert spaces, spectral theory of self-adjoint operators in Hilbert space, Fredholm determinant, unlimited operators.