The relativistic 4D space-time cover of Electrodynamics gives a roadmap for the creation of a potential function-based field theory within the algebraic structure of Octonion Algebra. Understanding the true algebraic nature of axial and polar vector types tells us which six Octonion basis components cover the electric and magnetic field types. Increasing the total dimension count from space-time 4 to Octonion 8 provides additional degrees of freedom required to accommodate Gravitation within the same structure. The Octonion framework for mathematical physics is presented in an algebraic covariant fashion. The Octonion Algebra forms for the analogous Maxwell’s Equations, physical fields, forces, work, energy and momentum conservation are presented. The importance of structuring the Octonion forms in an algebraic orientation covariant fashion is abundantly clear in this presentation.