In the 1970s Hirzebruch and Zagier produced elliptic modular forms with
coefficients in the homology of a Hilbert modular surface. They then
computed the Fourier coefficients of these forms in terms of period
integrals and L-functions. In this book the authors take an alternate
approach to these theorems and generalize them to the setting of Hilbert
modular varieties of arbitrary dimension. The approach is conceptual and
uses tools that were not available to Hirzebruch and Zagier, including
intersection homology theory, properties of modular cycles, and base
change. Automorphic vector bundles, Hecke operators and Fourier
coefficients of modular forms are presented both in the classical and
adèlic settings. The book should provide a foundation for approaching
similar questions for other locally symmetric spaces.