Includes bibliographical references and index.

There are two main approaches to the theoretical study of liquid crystals: continuum and molecular. The first, well covered in various good books (e.g. those by Chandrasekhar [1992]; de Gennes and Prost [1993]; Virga [1994]; Kleman and Lavrentovich [2003]; Stewart [2004]; Oswald and Pieranski [2005, 2006]; Barbero and Evangelista [2006]) considers anisotropic systems at macroscopic level and typically deals with optical and elastic properties as well as with many practical electrooptical applications of liquid crystals. At continuum level, liquid crystals are assumed to exist and their properties (e.g. elastic constants and viscosities) to be known, insofar as they are needed to parameterize the relevant equations. Molecules, phase transitions and spectroscopic properties are not normally taken into consideration. In this line of work computer simulations typically refer to a determination of the preferred orientation (director) or of the ordering tensor field that minimize the elastic free energy under a variety of boundary conditions, while dynamics is normally related to the solution of hydrodynamics equations for anisotropic fluids. The other main line of investigation deals.