This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura -- Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction.
This is a welcome addition to the literature in a field difficult to penetrate. This book should obviously be carefully studied by advanced students and by professional mathematicians in arithmetic algebraic geometry or (modern) number theory. -- Mathematical Reviews "Mathematical Reviews" The book's prose is clear, there are examples and exercises available, and, as always, the serious student should have a go at them: he will reap wonderful benefits. -- MAA Reviews "MAA Reviews"