The Laws of Classical Thermodynamics and the fundamental principles of Statistical Mechanics are reviewed with an emphasis on their logical structure. We discuss the universality of equilibrium fluctuations (Brownian Motion) and describe some contemporary results such as Jarzynski and Crooks Non-Equilibrium Work Identities. A brief review of Shannon Entropy revealsthe formal analogy between Thermodynamics and Information Theory: these two sciences must be coupled in order to understand and to exorcise Maxwell’s demon.