The method of moments (MOM), as introduced by R. F. Harrington more than 50 years ago, is reviewed in the context of the classic potential integral equation (PIE) formulations applied to both electrostatic (part 1) and electrodynamic, or full-wave, problems (part 2). A systematic treatment is presented based on the concept of "discrete Green's functions" ("GFs"). For the sake of simplicity and clarity, the developments are restricted to geometries composed of 2D metallic plates embedded in a homogeneous medium. Within this framework, original analytical developments are presented. They simplify the formulations and enable the implementation of point matching (PM) and Galerkin strategies without any need for a numerical evaluation of the involved multidimensional integrals. Simple MATLAB codes are provided, allowing the reader not only to reproduce but also to go beyond the pioneering results of Harrington, to whom this article pays an undisguised homage.