The simulation and optimization of processes assumes that the thermodynamic properties and phase equilibria of the mixtures concerned are well known. This knowledge is still based upon experimentation, but it is also the result of calculation methods based on the principles of thermodynamics that govern them, insure their coherence, and confer upon them a wide range of application. This text is concerned primarily with the description of these methods and their evolution. It is addressed to the student who wishes to apply the general principles he has learned, and to the engineer confronted with a choice, perhaps a difficult one, of the most appropriate method to solve his problem.