In the margins of a book, Pierre de Fermat (1601-65) claimed that he had a mathematical proof that was too large to fit the margin, but it was not until 1994 that other mathematicians proved what had become known as Fermat's Last Theorem. Saito (mathematics, U. of Tokyo) explained the proof in his 2009 Feruma Yoso, Japanese for Fermat Conjecture. The English translation, by Masato Kuwata, has been divided into two volumes. This volume--the first seven chapters and Appendix A--sets out the basic tools, and the second volume will contain the proof itself. Readers should have a background in number theory, commutative algebra, and the general theory of schemes. Annotation ©2014 Book News, Inc., Portland, OR (booknews.com)