In this chapter some of the mathematical methods and background of many variable theory are introduced. The cumulant expansion is defined and the relationship between cumulants and moments is described. Then the information correlation hierarchy is defined and its relationship to the cumulant expansion is made explicit. Finally, the linked cluster theorem, the Ursell development, and the cumulant expansion are shown to be direct consequences of a simple theorem about partitions. These techniques form the basis for investigations of the interdependency structure of a set of many variables.