In this chapter, we walk the reader through the different components of the GlobalMapping Directory. We begin with a discussion of the mathematical fundamentals, for which we use research article by Cantwell et al. [14] and the book [4] as our principle references. We then provide the reader with an overview of the primary data structures introduced within the GlobalMapping Directory (often done through C++ objects), and then present the major algorithms – expressed as either object methods or functions – employed over these data structures.