This paper describes random branching theory, a model for the solution structure of hyperbranched polymers. In this model, the hyperbranched polymer is assumed to be composed of units whose structure is simpler than the resulting polymer. These simple units can have any structure of chemical functionality, from monomers to linear chains or spherical particles. This paper outlines how this theory is constructed, describes the underlying assumptions and parameters, and summarizes the most basic form. It is shown how variations in the parameters change the behavior of the model, and described how to fit an experimental data series. This demonstrates how the model can be used to fit other data series, and how it can be used as a test for whether a polymer is randomly hyperbranched.