The book will focus on two major topics: (1) Andrew Wiles' recent proof of the Taniyama-Shimura-Weil conjecture for semistable elliptic curves; and (2) the earlier works of Frey, Serre, Ribet showing that Wiles' Theorem would complete the proof of Fermat's Last Theorem. In recognition of the historical significance of Fermat's Last Theorem, parts of the book will reflect on the history of the problem, while others will speculate on the future and describe some of the connections of Wiles's work with other parts of mathematics.