This volume contains the proceedings of the workshop held for the Applied Combinatorics program in March, 1988. The central idea of the workshop is the recent interplay of the classical analysis of q-series, and the combinatorial analysis of partitions of intergers. Many related topics are discussed, including orthogonal polynomials, the Macdonald conjectures for root systems, and related integrals. Those people interested in combinatorial enumeration and special functions will find this volume of interest. Recent applications of q-series (and related functions) to exactly solvable statistical mechanics models and to statistics makes this volume of interest to non-specialists. Included are several expository papers, and a series of papers on new work on the unimodality of the q-binomial coefficient.