Surface science has experienced an impressive growth in the last two decades. The attention has focussed mainly on single-crystal surfaces with, on the atomic scale, relatively simple and well-defined structures (for example, clean surfaces and such surfaces with limited amounts of additional foreign atoms and molecules). One of the most fundamental types of information needed about solid surfaces concerns the relative atomic positions. The geometrical arrangement of surface atoms influences most physical and chemical properties of surfaces, the list of which is long and includes a number of important technological applications: electronic surface states, contact potentials, work functions, oxidation, heterogeneous catalysis, friction, adhesion, crys­ tal growth etc. Surface crystallography - the determination of relative atomic positions at surfaces - has found a successful tool in Low-Energy Electron Diffraction (LEED): this technique has now determined the atomic positions for nearly a hundred surfaces, whether in the clean state or with additional foreign atoms or molecules. The main aim of this book is to publish a set of computer pro­ grams that has been specifically designed for and extensively used in surface crystallography by LEED. These programs are based on the dynamical (i.e.