What if there is structure amongst chaos? Here we delve into the realm of thermodynamics and statistical mechanics, where the motions of particles in a gas are dictated by probability, entropy, and temperature. From Boltzmann to Liouville, from Maxwell to Einstein and Dirac, statistical mechanics is a topic of physics that kept up with the changing times without losing its significance to the physics of gases. The Theory of Physics, Vol. 5 not only offers a mathematical introduction, but also an overview of the main considerations and cornerstones of thermodynamics and statistical mechanics, both nonrelativistic and relativistic, both classical and quantum. This book, intended for physics students and science enthusiasts alike, delves into the general overview and select applications of statistical mechanics. Select topics include, but are not limited to, the Liouville Theorem, relativistic kinetic theory, white dwarf stars, quark-gluon plasma, and an introduction to non-equilibrium noise. The book also assumes readers are familiar with the first four volumes of The Theory of Physics and mathematical statistics.