In this chapter, one of the most celebrated class of ECC schemes is introduced and their encoding and decoding algorithms explained. Reed-Solomon (RS) codes have found numerous applications in digital storage and communication systems. Examples include the famous RS (255, 223, 33) code for NASA space communications, shortened RS codes over GF(28) for CD-ROM, DVD and Terrestrial Digital HDTV transmission applications, an extended RS (128, 122, 7) code over GF(27) for cable modems, among many others.