This volume is devoted to the application of the integral equations method (IEM) and boundary elements method (BEM) to problems involving the sounding of geological media using direct current (DC). Adaptive mesh generation algorithms and numerical methods for solving a system of integral equations are discussed. Integral equations for the media, which contains piecewise linear contact boundaries, immersed local inclusions, and subsurface relief, are derived and solved numerically. Both 2.5D and 3D models with ground surface relief are considered. For 2D conductivity distributions, the influence of the relief on the interpretation of results is shown. Search solutions of the direct problem with ground surface relief are compared using the appropriate interpretation of results based on different inversion programs. Describes in detail the application of the BEM and IEM to 2.5D direct problems using ERT for geological media with a complex structure and having a large number of internal contact boundaries; Provides algorithms of grid generation of the boundaries that are adapted to the geometry of the media, the surface relief and the measurements of electrode arrays; Discusses the application of the BEM to 3D sounding problems using the ERT method; Illustrates the applications of inversion programs to synthetic data generated using the BEM in comparison with the original model and discusses the quality of the associated interpretation.