1. Introduction
2. The classical theory: Part I
3. The classical theory: Part II
4. Polarized Hodge structures and Mumford-Tate groups and domains
5. Hodge representations and Hodge domains
6. Discrete series and n-cohomology
7. Geometry of flag domains: Part I
8. Geometry of flag domains: Part II
9. Penrose transforms in the two main examples
10. Automorphic cohomology
11. Miscellaneous topics and some questions

This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another—an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. --- summary provided by publisher