Koblitz is in his element with this text. Much like Daniel Marcus's Number Fields, Koblitz develops a ground work to begin the study of elliptic curves. Here he builds upon the ancient problem of congruent numbers to help develop motivation for an in depth study of elliptic curves and modular forms. Not for the faint of (mathematical) heart, but a truly brilliant piece added to the number theoretic literature. A must own for those interested in advanced ideas behind elliptic curves.