There has been much progress in the computational approaches in the field of materials science during the past two decades. In particular, computer simula­ tion has become a very important tool in this field since it is a bridge between theory, which is often limited by its oversimplified models, and experiment, which is limited by the physical parameters. Computer simulation, on the other hand, can partially fulfill both of these paradigms, since it is based on theories and is in fact performing experiment but under any arbitrary, even unphysical, conditions. This progress is indebted to advances in computational physics and chem­ istry. Ab initio methods are being used widely and frequently in order to determine the electronic and/or atomic structures of different materials. The ultimate goal is to be able to predict various properties of a material just from its atomic coordinates, and also, in some cases, to even predict the sta­ ble atomic positions of a given material. However, at present, the applications of ab initio methods are severely limited with respect to the number of par­ ticles and the time scale of dynamical simulation. This is one extreme of the methodology based on very accurate electronic-level calculations.

1. Introduction.- 1.1 Computer Simulation as a Tool for Materials Science.- 1.2 Modeling of Natural Phenomena.- 2. Ab Initio Methods.- 2.1 Introduction.- 2.2 Electronic States of Many-Particle Systems.- 2.3 Perturbation and Linear Response.- 2.4 Ab Initio Molecular Dynamics.- 2.5 Applications.- 2.6 Beyond the Born-Oppenheimer Approximation.- 2.7 Electron Correlations Beyond the LDA.- References.- 3. Tight-Binding Methods.- 3.1 Introduction.- 3.2 Tight-Binding Formalism.- 3.3 Methods to Solve the Schrödinger Equation for Large Systems.- 3.4 Self-Consistent Tight-Binding Formalism.- 3.5 Applications to Fullerenes, Silicon and Transition-Metal Clusters.- References.- 4. Empirical Methods and Coarse-Graining.- 4.1 Introduction.- 4.2 Reduction to Classical Potentials.- 4.3 The Connolly-Williams Approximation.- 4.4 Potential Renormalization.- References.- 5. Monte Carlo Methods.- 5.1 Introduction.- 5.2 Basis of the Monte Carlo Method.- 5.3 Algorithms for Monte Carlo Simulation.- 5.4 Applications.- References.- 6. Quantum Monte Carlo (QMC) Methods.- 6.1 Introduction.- A. Molecular Dynamics and Mechanical Properties.- A.l Time Evolution of Atomic Positions.- A.2 Acceleration of Force Calculations.- A.2.1 Particle-Mesh Method.- A.2.2 The Greengard-Rockhlin Method.- References.- B. Vibrational Properties.- References.- C. Calculation of the Ewald Sum.- References.- D. Optimization Methods Used in Materials Science.- D.l Conjugate-Gradient Minimization.- D.2 Broyden's Method.- D.3 SA and GA as Global Optimization Methods.- D.3.1 Simulated Annealing (SA).- D.3.2 Genetic Algorithm (GA).- References.