Current understanding of different phases as well as the phase transitions between them has only been achieved following recent theoretical advances on the effects of dimensionality in statistical physics. P S Pershan explains the connection between these two separate areas and gives some examples of problems where the understanding is still not complete. The most important example is the second order phase transition between the nematic and smectic-A phase. Others include the relation between the several hexatic phases that have been observed and the first order restacking transitions between phases that were all previously identified as smectic-B, but which should more properly be identified as crystalline-B. Some relatively recent experimental developments on the discotic phase, liquid crystal surfaces and lyotropic phases are also included. The book includes 41 major reprints of some of the recent seminal work on the structure of liquid crystals. They are introduced by a brief review of the symmetries and other properties of liquid crystalline phases. In addition, there is a discussion of the differences between true liquid crystalline phases and others that were described as liquid crystalline in the early literature, but which have since been shown to be true three-dimensional crystals. The progression from the isotropic fluid, through the nematic, smectic, and various crystalline phases can be understood in terms of a systematic decrease in symmetry, together with an accompanying variation in structure is explained. A guide to the selected reprints and a sort of “Rosetta Stone” for these various phases is provided. The goal of this book is to explain the systematics of this progression to students and others that are new to this field, as well as to provide a useful handbook for people already working in the field. Contents:Phase Transitions and Continuous Symmetry BreakingNon-Perturbative Quantization of Topological SolitonsGauge Theories, including (the Infrared Problem in) Quantum ElectrodynamicsTriviality of λφ4Random Geometry (Quantum Gravity and Strings)Low-Dimensional QFT: Two-Dimensional Conformal Field Theory, Three-Dimensional (Gauge) Theories Readership: Applied physicists, physicists and chemists.