This is a graduate level course on principles of statistical mechanics and their applications to various physical systems. We will start from the Liouville’s theorem and head straight to microcanonical ensemble, canonical and then to grand canonical, going through various applications on the way (such as ideal gas and polymers). Then we will do quantum statistical mechanics with applications to solids, molecules, the Ising model in one dimension, chemical reactions, Fermi and Bose systems. An important application that we will go through is phase transitions. Finally, we will finish with an introduction to particle transport.