Statistical Description of Large Systems. Postulates of Statistical Physics -- The Different Statistical Ensembles. General Methods in Statistical Physics -- Thermodynamics and Statistical Physics in Equilibrium -- The Ideal Gas -- Indistinguishability, the Pauli Principle (Quantum Mechanics) -- General Properties of the Quantum Statistics -- Free Fermions Properties -- Elements of Bands Theory and Crystal Conductivity -- Bosons : Helium 4, Photons, Thermal Radiation.Statistical Physics bridges the properties of a macroscopic system and the microscopic behavior of its constituting particles, otherwise impossible due to the giant magnitude of Avogadro's number. Numerous systems of today's key technologies -- as e.g. semiconductors or lasers -- are macroscopic quantum objects; only statistical physics allows for understanding their fundamentals. Therefore, this graduate text also focuses on particular applications such as the properties of electrons in solids with applications, and radiation thermodynamics and the greenhouse effect.