The basic idea of induction logging is reviewed and the use of the geometrical factor is explained. The rigorous theory, based on Maxwell's equations, is then formulated for the simple 2-coil sonde, which is the basic building block for multicoil sondes. For a homogeneous conducting medium this theory leads to simple solutions for the fields and current density. These simple solutions are exploited in detail to build up a firm understanding of the skin effect phenomenon. The theory is then applied to nonhomogeneous media, and numerical results obtained through the use of the IBM 704 are presented. On the basis of this complete study some simple approximate results are presented which allow a rapid evaluation of skin effect in induction logging. The nonhomogeneous media considered in detail are 2 semi-infinite beds, thin beds bounded by adjacent formations, and an infinite bed with a borehole or invasion. It is shown that the borehole gives a negligible contribution to the skin effect.