Translation of part of the book [Netsugaku, tōkei-rikigaku]

About the Book: Statistical Mechanics: An Advanced Course with Problems and Solutions This book provides a series of concise lectures on the fundamental theories of statistical mechanics, carefully chosen examples and a number of problems with complete solutions. Modern physics has opened the way for a thorough examination of infra-structure of nature and understanding of the properties of matter from an atomistic point of view. Statistical mechanics is an essential bridge between the laws of nature on a microscopic scale and the macroscopic behaviour of matter. A good training in statistical mechanics thus provides a basis for modern physics and is indispensable to any student in physics, chemistry, biophysics and engineering sciences who wishes to work in these rapidly developing scientific and technological fields. The collection of examples and problems is comprehensive. The problems are grouped in order of increasing difficulty. Contents: 1. Principles of Statistical Mechanics. Microscopic states. Statistical treatment. The principle of equal weight and the microcanonical ensemble. The thermodynamic weight of a macroscopic state and entropy. Number of states and the density of states. Normal systems in statistical thermodynamics. Contact between two systems. Quasi-static adiabatic process. Equilibrium between two systems in contact. Fundamental laws of thermodynamics. The most probable state and fluctuations. Canonical distributions. Generalized canonical distributions. Partition functions and thermodynamic functions. Fermi-, Bose-, and Boltzmann- statistics. Generalized entropy. 2. Applications of the Canonical Distribution. General properties of the partition function Z(andbgr;). Asymptotic evaluations for large systems. Asymptotic evaluations and legendre transformations of thermodynamic functions. Grand partition function andlgr;. Partition functions for generalized canonical distributions. Classical configurational partition functions. Density matrices.