Pablo Shmerkin continues MIT's 18.156 Projection Theory course with lecture 14, introducing Bourgain's projection theorem, a central result in geometric measure theory. He presents it as the real-number analogue of the Bourgain-Katz-Tao projection theorem, situating it within the course's broader study of how sets and measures behave under orthogonal projections. The lecture builds on prior sessions, developing the statement and setup needed to prove the theorem, with an eye toward the combinatorial and Fourier-analytic techniques that distinguish the real case from the finite-field setting treated earlier in the course. Shmerkin works through the material at blackboard pace, typical of MIT OpenCourseWare's recorded graduate lectures, aimed at students already comfortable with measure theory and basic Fourier analysis. At 81 minutes, it is a full graduate-level session rather than a survey talk, continuing into a second part not covered here.