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These are the notes for a set of lectures delivered by the two authors at theLes Houches Summer School on `Complex Systems' in July 2006. They provide anintroduction to the basic concepts in modern (probabilistic) coding theory,highlighting connections with statistical mechanics. We also stress commonconcepts with other disciplines dealing with similar problems that can begenerically referred to as `large graphical models'.  While most of the lectures are devoted to the classical channel codingproblem over simple memoryless channels, we present a discussion of morecomplex channel models. We conclude with an overview of the main openchallenges in the field.

Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View