This course provides an introduction to non-relativistic quantum mechanics and to statistical mechanics. Introduction to quantum mechanics: probabilistic interpretation, time-dependent and time-independent Schroedinger equation, examples of solution of one-dimensional Schroedinger equations (free particles, wave packets, potential wells, harmonic oscillator). Algebraic solution for the harmonic oscillator. The formalism of quantum mechanics: Hilbert space, observables, properties of physical operators, generalized statistical interpretation, generalized indeterminacy principle, compatible observables, commutators, costants of motion, Dirac notation. Schroedinger equation in three dimensions for central potentials: variable separation, angular and radial quatione. Hydrogen atom. Angular momentum, commutation rules, eigenfunctions of the orbital angular momentum. Electron spin. Many-body systems. Identical particles: Pauli principle. Many-electron atoms, periodic table of the elements. Introduction to statistical mechanics Boltzmann statistics. Quantum statistics, Fermi-Dirac, Bose-Einstein. Paradoxes and interpretations of quantum mechanics: Bell inequalities. A glimpse on quantum computing.