These lectures were delivered at the University of Victoria, Victoria, B.C., Canada, in June of 2000, under the auspices of the Pacific Institute for the Mathematical Sciences. My originalintent was to describe the sequence of developments which began in the 1980's and has led to a united and automated approach to finding partition bijections. These developments,embodied in the sequence [5, 16, 8, 19, 14, 20] of six papers, in fact form much of the content of these notes, but it seemed desirable to preface them with some general background on the theory of partitions, and I could not resist ending with the development in [3], which concerns integer partitions in a wholly different way.The lecture notes were recorded by Joe Sawada, with such care that only a minimal buffng and polishing was necessary to get them into this form. My thanks go to Frank Ruskey, Florin Diacu and Irina Gavrilova for their hospitality in Victoria and for facilitating this work, and to Carla Savage for a number of helpful suggestions that improved the anuscript.