Lawrence D. Guth continues MIT's graduate course 18.156, Projection Theory, with a lecture on adapting the subject's core methods to Euclidean space while accounting for multiple scales. This is the third session in the sequence, building on earlier foundational material on projections and moving toward the multiscale techniques that recur throughout the field. The talk is blackboard mathematics at the graduate level, dense with definitions, lemmas, and proofs rather than illustrative examples, aimed at students who already have the course's prior two lectures under their belt. Guth works through the Euclidean setting methodically, tracking how estimates behave as scale changes. Runtime runs about eighty minutes, consistent with a full MIT OpenCourseWare lecture capture rather than a highlight reel.