The main goals are to deepen the knowledge of the basic principles of quantum mechanics and to consider some applications. The following subjects are considered: electron in a magnetic field: Landau levels, the Quantum Hall Effect, the Aharonov-Bohm effect; spin, spin in a magnetic field, spin resonance, addition of angular momenta; elements of quantum information; quantum computation and cryptography; identical particles; atomic states; fine structure of atomic levels; variational principle, helium atom, covalent bonding; semiclassical approximation; time-dependent perturbation theory; emission and absorption of radiation by atoms, selection rules and scattering theory.