These are notes for a graduate topics course offered on several occasions to a rather diverse group of doctoral students at Bowling Green State University. An earlier version of these notes was available through my Web pages for some time and, judging from the e-mail I've received, has found its way into the hands of more than a few readers around the world. Offering them in their current form seemed like the natural thing to do.

Although my primary purpose for the course was to train one or two students to begin doing research in Banach space theory, I felt obliged to present the material as a series of compartmentalized topics, at least some of which might appeal to the nonspecialist. I managed to cover enough topics to suit my purposes and, in the end, assembled a reasonable survey of at least the rudimentary tricks of the trade.

As a prerequisite, the students all had a two-semester course in real analysis that included abstract measure theory along with an introduction to functional analysis. While abstract measure theory is only truly needed in the final chapter, elementary facts from functional analysis, such as the Hahn–Banach theorem, the Open Mapping theorem, and so on, are needed throughout. Chapter 2, “Preliminaries,” offers a brief summary of several key ideas from functional analysis, but it is far from self-contained. This chapter also features a large set of exercises I used as the basis for additional review, when necessary. A modest background in topology is also helpful but, because many of my students needed review here, I included a brief appendix containing most of the essential facts.