The purpose of this textbook is to introduce the student to a basic area of mac- scopic physics, namely the statistical mechanical study of the different phases of matter, as well as the phase transitions between them. Although many books on statistical physics, for both equilibrium and non-equilibrium systems, are already available, they largely differ in contents. This generally re ects not only the diff- ent interests of their authors, but also the epoch in which they were written. For instance, the early books did usually devote much space to problems of the solid state, whereaslater ones do include, moreover,several aspects of the liquid state. At present, however, the main emphasis in physics is on soft matter (e. g. liquid cr- tals, colloids, polymers), and therefore these particular states of matter have also been includedin this volume. The main purposeof this textbookwill consist, hence, in providing its students with a rst introduction, within the general framework of equilibrium statistical physics, to a much larger variety of phases and phase tran- tions than was previously the case for textbooks of statistical mechanics. Many of these novel topics do, of course, deserve a more detailed study than the one which can be provided here. Indeed, in the spirit of a rst introduction, only very simple models of these phases will be given, but more detailed informationcan be found in the suggestions for further reading given in the References.