Generating functions (i.e. power series) have applications throughout enumerative and analytic combinatorics. In this thesis we present Genfunlib, a new Mathematica package containing a selection of implementations of symbolic methods related to generating functions. With Genfunlib one can find the generating functions for regular languages, compute the initial terms of a generating function, convert between generating function equations and recurrences, and find asymptotics. This thesis gives mathematical background, extensive documentation for Genfunlib, and tutorials.