This module provides a brief introduction to the theory of error-detecting and error-correcting codes, with special emphasis on the Reed-Solomon codes. Several different methods of defining codes and decoding are presented, and the parameters of these codes and their significance in practice are discussed. Simple, concrete examples are studied first before more general families of codes are considered. Throughout the module, concepts and results from Linear Algebra and (to a lesser degree) Abstract Algebra are used to define and analyze these codes.