I plan to discuss (without proofs) several topics in model theory more or less related to categoricity, i.e., uniqueness (up to isomorphism) of certain models. These topics will include Ryll-Nardzewski’s theorem characterizing countable categoricity, Morley’s theorem about uncountable categoricity, and the Baldwin-Lachlan theorem bridging those two topics. Along the way, I’ll present some related topics, like types, stability, and (if time permits) indiscernibility.