In this chapter, we discuss the fundamentals of statistical thermodynamics that will be useful for gas dynamics. Statistical thermodynamics connects the microscopic (quantum mechanical) properties of matter with its macroscopic (thermodynamic) properties. That is, with statistical thermodynamics, the thermodynamic properties of matter can be calculated from the results of the quantum mechanical calculations. The topics are Boltzmann distribution, molecular partition function, number of microstates and entropy, Bose-Einstein and Fermi-Dirac distributions and those in the dilute limit, vibrational temperature, rotational temperature, thermal de Broglie wavelength, canonical partition function, expressions for thermodynamic state variables in terms of canonical partition function, a closed system with constant temperature and volume, and dissociation and ionization equilibrium of nitrogen gas in the dilute limit (example).