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 Schrödinger Operator, Multidimensional Schrödinger Operator, Periodic Schrödinger Operator, Quantum Graphs, Non-linear Schrödinger Equation, References, Index.