The book provides a comprehensive introduction to error correction, covering both classical and modern material, including both block and stream (convolutional) codes. The book presents the needed mathematical material in a "just in time" approach. That is, when a topic is presented (such as group theory), this is immediately used in applications. Topics new to this edition include shortened codes, an inversionless BCH (Bose-Chaudhuri-Hocquenghem) decoding algorithm, approximate message passing, stochastic algorithms, bit-interleaved coded modulation, and more. Also covers classical BCH and Reed Solomon, Golay, Reed Muller, or Hamming codes these codes are still component codes in virtually every modern communication system and explores recently developed polar codes and fountain codes which are gaining importance.