Progress continues in the theoretical treatment of surfaces and processes on surfaces based on first-principles methods, i.e. without invoking any empirical parameters. In this book, the theoretical concepts and computational tools necessary and relevant for a microscopic approach to the theoretical description of surface science is presented, together with a detailed discussion of surface phenomena. This makes the book suitable for both graduate students and for experimentalists seeking an overview of the theoretical concepts in surface science. This second enlarged edition has been carefully revised and updated, a new chapter on surface magnetism is included, and novel developments in theoretical surface science are addressed.