In 1948, Claude Shannon proved that good error correcting codes exist. Unfortunately the beautiful algebraic codes that people talk about in math departments are not the ones he was referring to. Low-density parity-check (LDPC) codes, (re)invented in the 1990s, approach the theoretical limits of communication and have an efficient although non-optimal decoder that makes them usable in applications. I will give an introduction to error correcting codes and describe some of the interesting features of LDPC codes. I will assume little more than knowledge of basic linear algebra.