The macroscopic properties of gases, liquids or solids emerge as an average of the characteristics of their elementary constituents (either atoms or molecules). Accordingly, the statistical description of aggregates is based on the concept that macroscopic properties can be predicted by calculating the average value of any given physical observable which can be represented by microscopic (atomic or molecular) quantities.

The statistical approach aims at describing condensed matter at the most fundamental level (i.e. by taking explicit account of its atomic-scale structure), without however claiming to describe in detail all the degrees of freedom associated with its elementary constituents. This is an effective approach since it provides results of paradigmatic importance through a robust mathematical formalism; it is also an efficient means of predicting the emergent phenomena occurring in aggregates, providing their most fundamental explanation.

This Primer is divided into two parts, respectively focused on the statistical physics of classical and quantum systems. Each part contains a general chapter where basic concepts and related mathematics are developed leading to the Boltzmann, Fermi-Dirac, and Bose-Einstein distribution laws, which are the three cornerstones of statistical physics. Following this, distribution laws are applied to a thorough investigation of the thermal properties of paradigmatically important systems such as classical ideal gas, electron gas and phonon gas. Some specific phenomenologies are also discussed, the statistical foundations of which are treated in detail. These include, paramagnetism, blackbody radiation (photon gas), and the Bose-Einstein condensation.

This is a textbook for a standard introductory bachelor-level course in statistical physics and 2nd or 3rd year condensed matter and solid state courses.