AbstractThis chapter treats the subject of quantum error correction and fault-tolerant quantum computation. In particular, it presents the various representations of open-system quantum dynamics, insisting on the indistinguishability between different unravelings. Quantum error correction with discrete gates reacting to discrete error syndromes obtained from projective measurement can be seen as a form of quantum feedback that stabilizes a whole manifold of quantum states rather than a single one. The chapter gives a useful general introduction to the theory of stabilizers, which is key to the understanding of error correcting codes. It explains in full detail the principles behind the size of the overhead needed to make the entire quantum processor fault-tolerant, not just its memory.