Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists, and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains expository articles by program participants describing the present state of the art. Here researchers and graduate students will encounter Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.