We start this chapter with a brief review of some basic concepts. First in Section 1.1 we introduce the gallium arsenide (GaAs)/aluminum gallium arsenide (AlGaAs) material system which provides a very high quality two-dimensional conduction channel and has been widely used in meso-scopic experiments. Section 1.2 summarizes the free electron model that is commonly used to describe conduction electrons in metals and semiconductors. Next we discuss different characteristic lengths like the de Broglie wavelength, mean free path and the phase-relaxation length which determine the length scale at which mesoscopic effects appear (Section 1.3). The variation of resistance in the presence of a magnetic field is widely used to characterize conducting films. Both the low-field properties (Section 1.4) and the high-field properties (Section 1.5) yield valuable information regarding the electron density and mobility.

In Section 1.6 we introduce the concept of transverse modes which plays a prominent role in the theory of mesoscopic conductors and will appear repeatedly in this book. Finally in Section 1.7 we address an important conceptual issue that arises in the description of degenerate conductors, that is, conductors with a Fermi energy that is much greater than kBT. Normally we view the current as being carried by all the conduction electrons which drift along slowly. However, in degenerate conductors it is more appropriate to view the current as being carried by a few electrons close to the Fermi energy which move much faster. One consequence of this is that the conductance of degenerate conductors is determined by the properties of electrons near the Fermi energy rather than the entire sea of electrons.