Lawrence Guth continues MIT's 18.156 Projection Theory course with a lecture on sum-product theory, introducing tools from additive combinatorics and number theory. The session builds toward the sum-product phenomenon, the observation that a finite set of numbers cannot have both its sumset and its product set stay small, and develops the combinatorial and incidence-geometry machinery used to prove such bounds. Guth works through the argument at the board, connecting the material to the projection and incidence themes running through the rest of the course. At 77 minutes, this is a full graduate-level lecture assuming familiarity with earlier sessions on projections and incidence geometry. It belongs to a specialized sequence rather than a standalone popular talk, aimed at students already working through the course's cumulative arguments about combinatorial geometry and additive structure.