Abstract: If you take the collection of all lines through the origin in Cn, then this collection (somewhat tautologically) forms projective n-space. I’m sure you’re all wondering if there are other instances where the collection of a bunch of geometric objects can itself form an interesting geometric space (like a variety or a manifold). There are! When this happens, we call the resulting space a moduli space. I’ll give a gentle introduction to the topic, explaining what moduli spaces have to do with representable functors (with minimal category theory), and what you can do with them.