This thesis by Daniel Gottesman, titled "Stabilizer Codes and Quantum Error Correction," provides a comprehensive overview of the field of quantum error correction, focusing on stabilizer codes. The author acknowledges the guidance of his advisor, John Preskill, and the contributions of the QUIC collaboration members. The thesis is supported by various grants from the National Science Foundation, the U.S. Department of Energy, and DARPA. The thesis begins with an introduction to quantum computers and classical coding theory, highlighting the challenges of simulating quantum systems classically and the need for error correction in quantum computing. It then delves into the basics of quantum error correction, including the quantum channel, simple codes, and the properties of any quantum code. A key focus is the formalism of stabilizer codes, which are a group-theoretical structure that has proven particularly useful in constructing and understanding quantum codes. The thesis discusses various known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation. It also covers concatenated coding, upper and lower bounds on the existence of stabilizer codes, and the channel capacity. The thesis concludes with a partial list of known quantum error-correcting codes and their properties, along with appendices on quantum gates and a glossary of terms. The work is a significant contribution to the understanding and development of quantum error correction, providing a solid foundation for future research in this area.This thesis by Daniel Gottesman, titled "Stabilizer Codes and Quantum Error Correction," provides a comprehensive overview of the field of quantum error correction, focusing on stabilizer codes. The author acknowledges the guidance of his advisor, John Preskill, and the contributions of the QUIC collaboration members. The thesis is supported by various grants from the National Science Foundation, the U.S. Department of Energy, and DARPA. The thesis begins with an introduction to quantum computers and classical coding theory, highlighting the challenges of simulating quantum systems classically and the need for error correction in quantum computing. It then delves into the basics of quantum error correction, including the quantum channel, simple codes, and the properties of any quantum code. A key focus is the formalism of stabilizer codes, which are a group-theoretical structure that has proven particularly useful in constructing and understanding quantum codes. The thesis discusses various known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation. It also covers concatenated coding, upper and lower bounds on the existence of stabilizer codes, and the channel capacity. The thesis concludes with a partial list of known quantum error-correcting codes and their properties, along with appendices on quantum gates and a glossary of terms. The work is a significant contribution to the understanding and development of quantum error correction, providing a solid foundation for future research in this area.