This paper described a new algorithm, for “generalized mathematical formalism” of a “Spherically Symmetric Metric” ( ), that describes the Euclidean Metric, Minkowski Metric, Einstein Metric, or the Schwarzschild Metric; using Three (3) Metric Components & Three (3) Metric Coefficients; and likewise using a general algorithm which is composed of, Two (2) Metric Components & Two (2) Metric Coefficients. In this paper a general introduction to basic mathematical concepts for the geometric description of Euclidean “Flat-Space” Geometry and Non-Euclidean “Curved-Space” Geometry, and Spherically Symmetric Metric equations which are used for describing the causality and motion of the “Gravitational” interaction between mass with vacuum energy space, and the mass interaction with mass. This paper gives a conceptual and mathematical description of the differential geometry, of flat and curved space, space-time, or gravitational fields, using the “metric theory” mathematics of Euclidean, Minkowski, Einstein, and Schwarzschild, Spherically Symmetric metrics, and geodesic line elements.