Self-Dual Codes E. M. Rains and N. J. A. Sloane Information Sciences Research, AT&T Labs-Research 180 Park Avenue, Florham Park, NJ 07932-0971 May 19 1998 ABSTRACT Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems, bounds, mass formulae, enumeration, extremal codes, open problems. There is a comprehensive bibliography. A different version of this paper appeared in the Handbook of Coding Theory, ed. V. S. Pless and W. C. Huffman, Elsevier, Amsterdam, 1998, pp. 177-294. For the full version see http://www.research.att.com/~njas/doc/self.pdf (pdf) or http://www.research.att.com/~njas/doc/self.ps (ps)