Self-adjoint extensions of Hermitian operators Operators in Hilbert space Hermitian and self-adjoint operators Examples of construction of self-adjoint extensions Aharonov-Bohm effect Schrodinger equation in presence of the infinite solenoid Solenoid scattering cross-section Magnetic monopole in quantum mechanics Dirac potential Monopole harmonics Atom excitation by a slow monopole (Drell effect) Idea of 't Hooft-Polyakov monopole Berry phase Phase change under adiabatic change of Hamiltonian parameters Examples of calculation of the Berry phase: spin in the magnetic field, Aharonov-Bohm solenoid Supersymmetric quantum mechanics Bose and Fermi oscillators Witten quantum mechanics Factorization method Path integrals in quantum mechanics Euclidean Green function Path integral definition Calculation of elementary path integrals Instantons Tunneling in two-hole potential Instanton trajectory and zero mode Calculation of tunneling probability in approximation of a noninteracting instanton gas Preexponential factor calculation by means of Yost function Particle with friction in quantum mechanics Caldeira-Legget model Influence of friction on tunneling probability Path integral for a spin particle Path integral for coherent states Spin coherent states Spin tunneling in quasiclassical approximation