CONTENTS: Preface; A Bit of Quantum Mechanics; Operators in Hilbert Spaces; Spectral Theorem for Self-adjoint Operators; Compact Operators and the Hilbert-Schmidt Theorem; Elements of Perturbation Theory; Variational Principles; One-Dimensional Schroedinger Operator; Multidimensional Schroedinger Operator; Periodic Schroedinger Operator; Quantum Graphs; Non-linear Schroedinger Equation; References; Index.