This book gives a clear and logical exposition of the basic method of ensembles in Statistical Mechanics as developed by J.W. Gibbs. Beginning with the Liouville theorem, a brief but useful introduction to the classical statistical mechanics is provided. Then the quantum picture is outlined and basic postulates of quantum statistical mechanics are stated. The discussion of the symmetry of wave function and its effect on counting is given in detail. The relation between statistical mechanics and thermodynamics is worked out and the Gibbs paradox is discussed in a lucid way. The concept of entropy is related to the information theory. Various ensembles are constructed and used to derive the Bose-Einstein and Fermi-Dirac ideal gases, topics like liquid He, electrons in metals, and white dwarfs are given adequate coverage. Quantum Hall effect, random walk and Fourier analysis of a random fluctuation are devoted sufficient space to make it a useful and fascinating book. The book concludes with a discussion of the modern treatment of the critical phenomena and irreversible thermodynamics. Problems at the end of each chapter widen the area covered and also help to deepen the understanding of the material given. This book is written to introduce the subject to advanced undergraduates in physics and chemistry or to undergraduates of engineering classes. The present edition contains new appendix on ?Boundary Conditions?.