In certain organic substances, composed of anisotropic molecules, the transition from the crystalline to the liquid state takes place in two or more distinct steps. In these materials between the solid and liquid states additional phases are formed which exhibit both liquid-like behaviour (fluidity) and crystalline-like features (macroscopic anisotropy). The substances showing this phenomenon are called liquid crystals, the intermediate phases are termed liquid-crystalline phases or mesophases. By now thousands of liquid crystals are known and at least ten thermodynamically different mesophases are recognized.In all mesophases there is a long-range orientational order of the molecules. The preferred direction of the molecular alignment can be described with the help of a unit vector, the director, which, roughly speaking, is parallel to the "long axis" of the elongated molecules. In reality the orientation of the individual molecules fluctuates significantly in space and time, therefore it is more correct to define the director as a symmetry axis of the orientational distribution of the molecules. In certain mesophases this distribution has a rotational symmetry around the director (uniaxial phases), in others the distribution function depends on the azimuthal angle too (biaxial phases).The fluctuations around the director can be quantitatively described by an orientational order parameter which is 1 for a perfectly aligned system and 0 in the case of spherical symmetry, i.e. in the isotropic phase.The mesophases differ from each other regarding the positional order of the molecules (Fig. 1). In the nematic phase there is no long range positional order at all just as in isotropic liquids. Nematics are normally uniaxial, however biaxial nematics were discovered very recently. In the smectic phases the centre of masses of the molecules are concentrated in layers forming a one-dimensional density wave. In the smectic A and C phases there is no long-range positional order within the layers. The smectic A phase is uniaxial, the director (n) is parallel with the layer normal, 1. In the C phase the director is tilted with respect to the layer normal. This phase is biaxial although the deviation from uniaxiality is usually small. There are further smectic phases in which the molecules form two-dimensional lattices within the layers (ordered smectic phases). The difference between ordered