Lawrence Guth continues MIT's course 18.156, Projection Theory, with a lecture on the Bourgain-Katz-Tao projection theorem from the early 2000s. Guth frames it as the first major result in the field to move past the two basic techniques introduced back in lecture 2, and works through the argument that lets the theorem say something stronger than those earlier methods could reach. The lecture assumes familiarity with the course's groundwork on projections of sets in the plane and builds the proof step by step on the board, the standard format for this OCW series. It sits within a graduate-level sequence on geometric measure theory and combinatorics, aimed at students who already have the earlier lectures under their belt rather than newcomers to the subject.