This is the first text to be written on the topic of Self-Field Theory (SFT), a new mathematical description of physics distinct from quantum field theory, the physical theory of choice by physicists at the present time. SFT is a recent development that has evolved from the classical electromagnetics of the electron’s self-fields that were studied by Abraham and Lorentz in 1903-04. Due to its bi-spinorial motions for particles and fields that obviate uncertainty, SFT is capable of obtaining closed-form solution for all atomic structures rather than the probabilistic solutions of QFT.