The article discusses the theoretical foundations and numerical methods for solving the direct and inverse problems of magnetotelluric sounding (MTS) based on Maxwell’s equations. A mathematical description of the geoelectrical model consisting of horizontally layered isotropic media with different electrical resistivities is presented. The inverse problem is solved using the optimal control approach and the adjoint equation method. A gradient iterative algorithm is developed to reconstruct the distribution of electrical conductivity from observational MTS data. Numerical experiments confirm the stability and convergence of the proposed method: as the number of iterations increases, the objective functional decreases significantly, and the reconstructed parameters closely approach the true values. The results demonstrate the effectiveness of the MTS technique in interpreting geoelectrical structures and its practical importance for assessing the deep-layer electrophysical properties of the Earth’s crust in geophysical exploration.