Lawrence Guth continues MIT's graduate course 18.156, Projection Theory, with a lecture on the Balog-Szemeredi-Gowers theorem, a core result in combinatorial number theory. Guth presents this as the last tool the course builds before moving on to applications, situating it alongside earlier material on sum sets and additive combinatorics. The lecture works through the theorem's statement and proof at the board, the standard format for this OCW series, aimed at graduate students already fluent in the course's earlier lectures on incidence geometry and projections. It is a single session within a multi-lecture sequence, not a standalone popular talk, and assumes the technical vocabulary built up over the semester. The pace is dense and proof-driven, typical of advanced MIT math courses recorded for OpenCourseWare.