1. The Bergman Spaces
2. The Berezin Transform
3. A[superscript p]-Inner Functions
4. Zero Sets
5. Interpolation and Sampling
6. Invariant Subspaces
7. Cyclicity
8. Invertible Noncyclic Functions
9. Logarithmically Subharmonic Weights

Fifteen years ago, most mathematicians who worked in the intersection of function theory and operator theory thought that progress on the Bergman spaces was unlikely, yet today the situation has completely changed. For several years, research interest and activity have expanded in this area and there are now rich theories describing the Bergman spaces and their operators. This book is a timely treatment of the theory, written by three of the major players in the field.