During the last thirty years metal surface physics, or generally surface science, has come a long way due to the development of vacuum technology and the new surface sensitive probes on the experimental side and new methods and powerful computational techniques on the theoretical side. The aim of this book is to introduce the reader to the essential theoretical aspects of the atomic and electronic structure of metal surfaces and interfaces. The book gives some theoretical background to students of experimental and theoretical physics to allow further exploration into research in metal surface physics. The book consists of three parts. The first part is devoted to classical description of geometry and structure of metal crystals and their surfaces and surface thermodynamics including properties of small metallic particles. Part two deals with quantum-mechanical description of electronic properties of simple metals. It starts from the free electron gas description and introduces the many body effects in the framework of the density functional theory, in order to discuss the basic surface electronic properties of simple metals. This part outlines also properties of alloy surfaces, the quantum size effect and small metal clusters. Part three gives a succinct description of metal surfaces in contact with foreign atoms and surfaces. It treats the work function changes due to alkali metal adsorption on metals, adhesion between metals and discusses the universal aspects of the binding energy curves. In each case extensive reference lists are provided.