In this lecture from the Yale Quantum Institute Course on Quantum Error Correction, held at Yale University in July 2025 in partnership with North Carolina A&T, Yongshan Ding covers quantum codes, the stabilizer formalism, and how these structures support fault tolerant quantum computation. Building on the introductory session on classical and quantum error correction, the lecture develops the mathematical framework used to detect and correct errors in quantum systems without destroying the quantum information being protected. It is part of a short course intended to give participants a working grasp of the theory and practice of quantum error correction as applied to real quantum computing hardware.