This thesis is a study of several different through related approaches to deriving q-series identities. Emphasis is placed on the role played by solutions of q-difference equations and expansions in symmetric polynomials. The polynomial expansions are obtained by applying q-umbral operators. The expansions are invariants of q-series and immediately give the structure of their transformation groups and show connections between various functions. Applications to continued fractions and to the theory of partitions are made including an extension of the 1991 Alladi-Gordon generalization of I. Schur's 1926 partition theorem.
