In this introductory chapter several basic concepts, relevant for mesoscopic electron transport, will be described. The aim is to provide a basis for several of the following Chapters of this volume. We, therefore, describe in the first Section various aspects of electron quantum transport in twodimensional electron gases. This includes an estimate of typical material parameters as well as comments on the fabrication. We then describe the quantization of the conductance in point contacts and the edge state picture of the Quantum Hall effect. In the second Section we describe the theory of single—electron tunneling in systems with strong charging and Coulomb-blockade effects. Here we restrict ourselves to the simplest case where low order perturbation theory is sufficient. We first discuss metallic low-capacitance junction systems and then indicate the relevant extensions when dealing with transport through quantum dots with discrete levels. Many further, equally important aspects of mesoscopic transport can not be covered here. Examples are interference and weak localization effects, level statistics or the many body description of solids. Fortunately, some of those will be covered in the more specialized Chapter of this volume.