Recent years have witnessed tremendous progress in the theoretical treatment of surfaces and processes on surfaces. A variety of surface properties can now be described from first principles, 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. Based on the fundamental theoretical entity, the Hamiltonian, a hierarchy of theoretical methods is introduced. Furthermore, a detailed discussion of surface phenomena is given and comparisons made to experimental results made, making the book suitable for both graduate students and for experimentalists seeking an overview of the theoretical concepts in surface science.