Induction well logging is a method for measuring the electrical conductivity of the rock around a borehole, with this information in turn being used to estimate the content of oil or gas in the rock. Since the development of induction well logging in the late 1940s, it has become the standard method used, primarily because of its simplicity of design. Now, 40 years later, and with the availability of new technology both in tool construction and in mathematical analysis, this book examines our understanding of induction logging in mathematical detail, and suggests how to develop more useful applications. The first part of the book reviews the theoretical basis of the electromagnetic methods for determining earth conductivity. All such methods are based fundamentally on Maxwell's equations. In practice, however, induction well logging is based on end-state behaviour for electromagnetic fields at low frequencies. Thus, the wave equation is developed for the extreme, low frequency condition, which produces many specific algebraic results of use in equipment design.