This textbook gradually introduces students to the statistical mechanical study of the different phases of matter and to the phase transitions between them. It uses simple yet fully detailed models of both hard and soft matter systems to demonstrate core concepts, developing the subject matter in a thorough and accessible pedagogical manner throughout. Starting from an introduction to basic thermodynamics and statistical physics, the book progresses from ideal, non-interacting systems to real systems exhibiting classical interactions and phase transitions. It concludes with a selection of more advanced topics, such as the renormalisation group approach to critical phenomena, the density functional theory of interfaces, and kinematic aspects of the phase transformation process. This updated second edition features a considerably expanded study of the topology of the phases, including applications to modern problems such as topological defects of nematic liquid crystals and the topological phase transition of a two-dimensional spin system. Along with a complete introductory overview of the theory of phase transitions, this textbook provides students with ample material for deeper study. References include suggestions for more detailed treatments and six appendices supply overviews of the mathematical tools employed in the text.