Statistical thermodynamics plays a vital linking role between quantum theory and chemical thermodynamics, yet students often find the subject unpalatable. In this text, the authors set out to overcome this by emphasizing the concepts involved, in particular demystifying the partition function. They do not get bogged down in the mathematics that are essential for a profound study of the subject but which can confuse the beginner. Strong emphasis is placed on the physical basis of statistical thermodynamics and the relations with experiment. After a clear exposition of the distribution laws, partition functions, hear capacities, chemical equilibria and kinetics, the subject is further illuminated by a discussion of low-temperature phenomena and spectroscopy. The coverage is brought up to date with a chapter on computer simulation and a final section which ranged beyond the narrow limits usually associated with student texts to emphasize the common dependence of macroscopic behaviour on the properties of constituent atoms and molecules. Since first published in 1974 as "Entropy and Energy Levels", this work has been revised and updated. It is intended for undergraduates and graduates in chemistry, general physics and statistical mechanics.