The primary goal of this book is to summarize the current level of accumulated knowledge about the physical structure of solid surfaces with emphasis on well-defined surfaces at the gas-solid and vacuum-solid interfaces. The intention is not only to provide a standard reference for practitioners, but also to provide a good starting point for scientists who are just entering the field. The presentation in most of the chapters therefore assumes that the typical reader will have a good undergraduate background in chemistry, physics, or materials science. At the same time, coverage is comprehensive and at a high technical level with emphasis on fundamental physical principles. This first volume in a new series is appropriately devoted to the physical structure of surfaces, knowledge of which will be essential for a complete understanding of electronic properties and dynamical processes, the topics of the next two volumes in the series. The volume is divided into four parts. Part I describes the equilibrium properties of surfaces with emphasis on clean surfaces of bulk materials. Part II provides an introduction to some of the primary experimental methods that are used to determine surface crystal structures. Part III gives an overview of the vast topic of the structure of adsorbed layers. The concluding Part IV deals with the topics of defects in surface structures and phase transitions.