Part 1 Introduction: the many particle Schroedinger equation; the Born-Oppenheimer approximation; the potential energy surface. Part 2 Physisorption: the Van der Waals interaction; the repulsive interaction; experimental studies. Part 3 Bulk metal properties: the electron gas; electrons in a periodic potential; one-dimensional band theory. Part 4 The interacting electron gas: Hartree and Hartree-Fock theory; density functional theory; Jellium; work function; surface energy. Part 5 The Newns-Anderson model: chemisorption; dynamics. Part 6 Lang-Williams theory of chemisorption. Part 7 The Scandanavian School. Part 8 Slab calculations: the LAPW method. Part 9 Cluster calculations: generalized valence bond; Hartree-Fock and configuraton interaction; local density methods. Part 10 The effective medium theory: derivation of the method; atomic chemisorption; molecular chemisorption.