A tutorial treatment of the main concepts of the physics of crystal surfaces. Emphasis is placed on simplified calculations and the corresponding detailed analytical derivations, that are able to throw light on the most important physical mechanisms. More rigorous techniques, which often require a large amount of computer time, are also explained. Wherever possible, the theory is compared to practice, with the experimental methods being described from a theoretical rather than a technical viewpoint. The topics treated include thermodynamic and statistical properties of clean and adsorbate-covered surfaces, atomic structure, vibrational properties, electronic structure, and the theory of physisorption and chemisorption. The whole is rounded off with new excercises.