Understanding the macroscopic properties of liquid crystals and their phase transitions in terms of molecular models can only be achieved using computer simulations, possibly with the complement of approximate statistical mechanical theories. Although liquid crystal simulations are obviously based on the same general Monte Carlo and molecular dynamics techniques used for other fluids, they present several problems and peculiarities related to the intrinsic properties of liquid crystals, such as long-range order and anisotropy, which require separate treatment. This in turn requires the development of suitable algorithms to calculate static properties such as order parameters, correlation functions, elastic constants and generally tensor observables, as well as dynamic quantities such as diffusion tensors, viscosities, susceptibilities, etc. It is now also possible to examine the topological defects characteristic of various liquid crystals and study their basic structure, and even perform direct simulations of simple devices and displays at the microscopic level. Another set of problems is related to the need to predict the properties of liquid crystals from molecular models. This involves the determination of phase behaviour, phase transitions and their characteristics, and requires the development of intermolecular potentials for modelling the essential molecular characteristics of mesogens and performing large-scale simulations, with particle numbers often an order of magnitude higher than those used in simple fluid simulations. This in turn requires the exploitation of state-of- the-art computing resources, in particular parallel computing techniques with the development of appropriate algorithms. This school aims to provide up-to-date coverage of all the issues listed above, considering the various techniques, model systems (from lattice to hard particles and Gay-Berne to atomistics) for thermotropics, lyotropes and some liquid crystals of biological interest.