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This book presents principles, basic concepts and application of Statistical Mechanics. The standard undergraduate syllabus in Physics includes in introductory course in Statistical Mechanics, while the postgraduate course in Statistical Mechanics is much more extensive in scope and this book is intended for both categories of students. Students often take difficulty in the problems on Statistical Mechanics. So for their convenience, a sufficient number of solved problems are incorporated after each topic. In fact around the solved problems are given in this book. Broadly it covers the following topics: Basis of Statistical Mechanics Elements of Ensemble Theory Classical or Maxwell-Boltzmann Statistics Foundation of Quantum Statistics Fermi-Dirac Statistics Bose-Einstein Statistics Interacting Classical Systems: The Method of Cluster Expansion Introduction to Phase Transition