This graduate textbook introduces the theory of error-correcting codes, working over an arbitrary finite field; algebraic curves, working over an algebraically closed field; geometry over a finite field; and constructions of algebraic geometry codes. The Russian authors discuss the Riemann-Roch theorem, the theory of elliptic curves, asymptotic bounds for the number of points on a curve, calculation of the number of divisors with prescribed properties, towers of curves with many points, and asymptotic lower bounds of algebraic geometry origin. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)