Tobias Holck Colding continues MIT's 18.100B Real Analysis course with a lecture on sequential compactness in metric spaces. He proves the Bolzano-Weierstrass theorem in this general setting, showing that a sequence contained in a compact subset of a metric space must have a convergent subsequence. The lecture builds the argument through standard analysis tools: subsequence extraction, limit points, and the relationship between compactness and sequential compactness. Running 84 minutes, it is delivered in the chalk-and-talk style typical of MIT OpenCourseWare recordings, with Colding working through definitions and proofs step by step at the board. The material sits in the middle of the course's development of compactness, following earlier lectures on open and closed sets and preceding applications to continuity and uniform convergence. Suited to students who have already met basic metric space topology and want a rigorous treatment of why compactness guarantees convergent subsequences.