This paper presents the theoretical basis for more accurate calculation of currents and potentials along large mesh earthing conductors or earthing systems as earthing conductor discharge fields in homogeneous soil. It takes into account the influence of harmonic time changes of the power source. The calculation is limited to low frequencies. The introductory chapter highlights the need for more realistic and accurate analysis of large earthing systems as a prerequisite for optimal and safe earthing of power plants. To solve the task set, the development of a new method and an approach to the problem using the theory of electromagnetic fields and the theory of electric circuits are proposed. The second chapter contains an overview and commentary on several relevant methods that are currently used in the analysis of so-called non-equipotential earthing conductors for quasi-stationary conditions. The determination of the distribution of transverse leakage currents and longitudinal currents along underground bare conductors in all of the above methods is based on the segmentation of these conductors. The methods differ significantly from each other in the way in which the mutual impedances of the segments are included in the calculation and in the expression used to determine the impedance value. The third chapter presents general relations for the responses of a horizontal and vertical infinitesimal electric dipole in an infinite homogeneous conducting medium. Immediately after this, analogous relations are given for a dipole in a lower homogeneous conducting half-space with air (or any other medium) as the upper medium. These last relations, which contain Sommerfeld integrals, are quite general within the framework of the thin wire assumptions and are not frequency-limited. The fourth chapter presents analytical approximations of the Sommerfeld integrals that are valid in a certain low-frequency range. In addition, even simpler analytical expressions are developed that can be used in calculating the mutual impedances of segments for quasi-stationary conditions. However, they are valid, with a certain error, for a limited range of distances between the source point and the observation point. The limiting distances are shown in the diagrams as functions of the specific electrical resistivity of the soil with a given percentage error of the absolute value of the approximation, and for a frequency of 50 Hz. In Chapter 5, definitions of different mutual impedances between two thin, cylindrical, finitely long and uninsulated segments located in a homogeneous conducting unbounded medium or in a conducting half-space are given and discussed. Due to the variability of the amount of current along such a segment, the classical definition of mutual impedance is not applicable. Instead of the concept of general (generalized) mutual impedances, a concept with separate longitudinal and transverse mutual impedances is introduced. They use the average values of the current or potential of the segment in their definition expressions, respectively. In Chapter 6, the development of a mathematical model for calculating the distribution of potentials and currents on a mesh non-equipotential grounding conductor buried in a homogeneous conducting half-space is presented in detail. In the process of solving the IDJ of the alternating electromagnetic field of a system of thin conductors, the matrix method with the Galerkin method and the linear function of approximation of the longitudinal current of the segment is first applied. The resulting system of linear segment equations was then modified and the concept of longitudinal and transverse mutual impedances of segments, described in Chapter 5, was introduced. Then, a special matrix relation was found which, in the linear approximation of the current, connects the segment currents (longitudinal and transverse) and the node currents imposed on the grounding system. Finally, this matrix relation allows setting up a system of linear algebraic equations with the node potentials as the only unknowns. The distribution of currents across the grounding system is determined after the node voltage vector is determined using the matrix relations of the theory of electric circuits and a special form of the node-branch incidence matrix. After determining the transverse currents, it is possible to calculate the potentials on the ground surface. Chapter 7 refers to analytical and numerical procedures for determining the values of the segment self-impedances as well as different types of mutual impedances between two straight segments of grounding conductors. Chapter 8 presents a block flow diagram of a computer program for calculating large mesh grounding conductors or grounding systems. In Chapter 9, several characteristic examples illustrate some of the possibilities offered by the computer program in the analysis of large earthing systems. A comparison of some available measurement results with results calculated using various theoretical models is also carried out. The conclusion highlights the scientific contribution of this work, and some general recommendations for the calculation and design of large earthing systems are also given.