  Controlling operational errors and decoherence is one of the major challenges
facing the field of quantum computation and other attempts to create specified
many-particle entangled states. The field of quantum error correction has
developed to meet this challenge. A group-theoretical structure and associated
subclass of quantum codes, the stabilizer codes, has proved particularly
fruitful in producing codes and in understanding the structure of both specific
codes and classes of codes. I will give an overview of the field of quantum
error correction and the formalism of stabilizer codes. In the context of
stabilizer codes, I will discuss a number of known codes, the capacity of a
quantum channel, bounds on quantum codes, and fault-tolerant quantum
computation.
