Structural stability is of fundamental importance inmaterials science. Up-to-date information on the theoreticalaspects of phase stability of materials is contained in thisvolume. Most of the first-principles calculations are basedon the local-density approximation (LDA). In contrast, thisvolume contains very recent results of "going beyond LDA",such as the density gradient expansion and the quantumMonte-Carlomethod.Following the recently introduced theoretical methods forthe calculation of interatomic potentials, forces acting onatoms and total energies such as the Car-Parrinello, theeffective-medium and the bond-ordermethod, attempts havebeen made to develop even more sophisticated methods such asthe order-N method in electronic-structure calculations. Thepresent status of these methods and their application toreal systems are described.In addition, in order to study the phase stability atfinitetemperatures, the microscopic calculations have to becombined with statistical treatment of the systems todescribe, e.g. order-disorder transitions on the Si(001)surface or alloy phase diagrams. This book contains examplesfor this type of calculations.