This work is a comprehensive treatment of recent developments in the
study of elliptic curves and their moduli spaces. The arithmetic study
of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and
the modern theory was erected by Eichler-Shimura, Igusa, and
Deligne-Rapoport. In the past decade mathematicians have made further
substantial progress in the field. This book gives a complete account of
that progress, including not only the work of the authors, but also that
of Deligne and Drinfeld.