The phase behaviour of materials and their thermodynamic properties are a central subject in all fields of materials research. The first Volume of the work, meant for graduate students in chemistry, geology, physics, and metallurgy, and their engineering counterparts, is split up in three levels, such that from level to level the portion and importance of thermodynamics and mathematics are increased. In the ground level it is shown that the basic principles of phase equilibria can be understood without the use of thermodynamics be it that the concept of chemical potential is introduced right from the beginning. The intermediate level is an introduction to thermodynamics; culminating in the Gibbs energy as the arbiter for equilibrium demonstrated for systems where the phases in equilibrium are pure substances. In the third level the accent is on binary systems, where one or more phases are solutions of the components. Explicit relationships between the variables are derived for equilibria involving ideal mixtures and ideal dilute solutions. Non-ideal systems are treated from three different angles geometrically, analytically, and numerically.Throughout the work high priority is given to the thermodynamic assessment of experimental data; numerous end-of-chapter exercises and their solutions are included. The work is useful for scientists as an introduction and a reference book.