This text contains the proceedings of the Conference on Coding Theory, Cryptography and Number Theory held at the U.S. Naval Academy during October 25-26, 1998. It consists of elementary and advanced aspects of coding theory and cryptography. The coding theory contributions deal mostly with algebraic coding theory. The emphasis is on geometric Goppa codes, but there is also a paper on codes arising from combinatorial constructions. There are both historical and mathematical papers on cryptography. Several of the contributions on cryptography describe the work done by the British and their allies during World War II to crack the German and Japanese ciphers. Also described are some mathematical aspects of the Enigma rotor machine and more recent research on quantum cryptography. Moreover, there are two papers concerned with the RSA cryptosystem and related number-theoretic issues.