Abstract: In order to realize highly accurate calculations for the theories of eleotromagnetism(e. g., microwave directive coupler et. al), the "geometrization number theory eliminating singularity approach" is suggested. This paper, the first one in the paper series, gives a general theoretical formulation of the GNES approach. And a fairly general class of exact, asymmetric, non-Hermitian, singular integral equation systems is formulated, with the aid of the Ω-series theory developed by us. The general formal solutions, the details of the GNES approach, techniques and numerical results will be presented in the succeeding papers.

Key words: Thery of electromagnetism, Singulau integral equation system, Eliminating singularity, Number theory, Geometrization