This primer provides an introduction to the subject of surfaces at the level of undergraduates and first year postgraduates. There are three chapters, the first concerns basic thermodynamic material used to understand the properties of surfaces including; surface tension, Gibbs adsorption, surface pressure and surface phase equilibria, surfactants and micelles, wetting, detergency, and contact angle. The second chapter concentrates on gas adsorbtion at solid surfaces and covers topics including adsorbtion, Langmuir isotherms, heats of adsorbtion, BET isotherms, physisorbtion, chemisorbtion, precursor adsorbtion kinetics, well-defined surfaces, UHV, surface sensitivity and selectivity, surface diffusion and electrons interacting with matter. The final chapter contains a series of worked examples and problems, bringing together the various strands developed in Chapters 1-3 in order to elucidate surface phenomena. The book is unique in its mix of 'Classical' and 'Modern' surface science and should be relevant to physicists, chemists and material scientists.