Book excerpt: The Second Law of Thermodynamics, that entropy increases, is arguably the most fundamental law of nature. And yet for some, entropy itself is a mystery, the cause of confusion and misunderstanding. How can it be that something so fundamental and universal be so hard to grasp? How can it have happened that thoughtful people appreciate the significance and universal applicability of the Second Law without understanding the nature of entropy, its sole concern? This book presents a coherent formulation of all aspects of thermodynamics and statistical mechanics with entropy as the unifying theme. This includes formulating equilibrium theory from first principles, and explaining the role of the Second Law in establishing the equilibrium state. It also includes establishing the foundations of non-equilibrium theory by generalizing the concept of entropy in an appropriate way. Finally, it addresses the relationship between classical and quantum statistical mechanics by invoking the collapse of the wave function into entropy states. A secondary purpose is to increase the understanding of entropy and the Second Law, and to correct misapprehensions and errors that have arisen over the years. By consolidating these approaches into a coherent and self-contained framework, it is intended to improve the understanding of this fundamental and fascinating area of physics. Thermodynamics and statistical mechanics are such important subjects that students, academics, and researchers need to have the fundamental concepts clearly and concisely presented, as simply as possible, and as part of a unified whole. To this end, the book motivates the mathematical theorems and derivations with detailed physical explanation, applications, and concrete examples.