Pablo Shmerkin continues MIT's graduate course 18.156, Projection Theory, with the third installment on the Bourgain projection theorem. This session focuses on the role of robust estimates in multiscale arguments, the technical machinery used to control how sets and measures behave across different scales when proving projection bounds. As part three of a multi-lecture treatment, it assumes familiarity with the setup and earlier estimates developed in the preceding sessions and pushes further into the proof's harder technical steps. The lecture is delivered in MIT's standard OCW chalkboard format, aimed at graduate students in harmonic analysis, fractal geometry, or geometric measure theory who are following the course sequentially. It sits within a specialized area connecting Fourier analysis, combinatorics, and dimension theory, and is best suited to viewers already working through the course rather than newcomers to the topic.