Remarks about the PCP Theorem, Dinur's proof of it, and a full statement of the theorem, including its hardness-of-approximation interpretation and its proof-checking interpretation. Lecture 27a of "CS Theory Toolkit": a semester-long graduate course on math and CS fundamentals for research in theoretical computer science, taught at Carnegie Mellon University. Resource for this lecture: Course on "The PCP Theorem and Hardness of Approximation" by O'Donnell and Guruswami, Taught by Ryan O'Donnell ( ~odonnell) Course homepage on CMU's Diderot system: Thumbnail photo by Rebecca Kiger ( )