This second edition of the popular textbook is intended for all undergraduate students in physics, with some background in thermodynamics. The basic intention of the author is maintained: to present a book for those studying statistical mechanics for the first time. The unique presentation starts off with the principles, elucidating the well-developed theory, and only thereafter the application of theory. Calculations on the main steps are detailed, leaving behind minimal gaps. The author emphasizes with theory the link between the macroscopic world (thermodynamics) and the microscopic world.The book begins with a study of three situations — the closed system and the systems in thermal contact with a reservoir — in order to formulate the important fundamentals: entropy from Boltzmann formula, partition function and grand partition function. Through the presentation of quantum statistics, Bose statistics and Fermi-Dirac statistics are established, including as a special case the classical situation of Maxwell-Boltzmann statistics. A series of examples follow: the harmonic oscillator, the polymer chain, the two-level system, bosons (photons, phonons, and the Bose-Einstein condensation) and fermions (electrons in metals and in semiconductors). The treatment of bosons and fermions is expanded with a detailed comparison of their thermal behaviors. A study on neutron stars, a pure fermion system, is now included. The concepts of distribution and fluctuations are also briefly discussed, and an important neglected problem is explained: the equivalence between the sum of a series and the value of the associated integral, teaching further insights on Bose-Einstein condensation. A compact historical note on influential scientists forms the concluding chapter.This book will serve as a vital resource for undergraduates taking their first foray into statistical mechanics, setting a strong foundation for more advanced topics in their studies.