Tobias Holck Colding continues MIT's 18.100B Real Analysis course by extending concepts from the real line to general metric spaces. He covers sequences, convergence, and Cauchy sequences in this broader setting, then introduces balls, bounded sets, and the definitions of open and closed subsets. The lecture builds directly on prior material, translating intuitions built on the real number line into the more abstract language of metric spaces, with worked definitions and examples developed on the board. Running 81 minutes, it is a standard installment in MIT's undergraduate real analysis sequence, aimed at students who already have the earlier lectures on sequences and Cauchy sequences in hand. The pace is deliberate and proof-driven, typical of MIT OpenCourseWare's recorded classroom lectures, with Colding working through definitions and their consequences at the board rather than through slides.