Description of a spacetime geometry that allows representing the mutual induction of electric energy and magnetic energy within elementary particles in motion in conformity with Maxwell's equations. This new geometry draws attention to the fact that adiabatic kinetic energy is continuously induced in all elementary particles captive within atomic structures, which is linked to an atomic axial mass variation effect related to the local intensity of the gravitational gradient, which sheds an entirely new light on gravitation, since it can be demonstrated that these least action electromagnetic equilibrium states determine the local intensity of the gravitational gradient on top of determining the orbital resonance states revealed by Quantum Mechanics. This book explores the foundations of an electromagnetic mechanics of elementary particles whose laws apply by structure to the sub-microscopic level, the macroscopic level and the astronomical level, thus allowing the reconciliation of electromagnetism, Quantum Mechanics, Relativistic Mechanics and gravitation.