The concepts and relations pertinent to the solution of many thermodynamic problems encountered in multi-phase, multi-component systems are developed in this volume. Emphasis is placed on a comprehension and development of general expressions for solving such problems, rather than ready-made equations for particular applications. The first half of the book is devoted to defining the thermodynamic functions and to generating the fundamental relations relevant to chemical systems at equilibrium. The second half concentrates on the application of these relations to real systems and the methods which can be used to obtain additional connections. Throughout, the methods of Gibbs are used with emphasis on the chemical potential.