Topology is a field of math which concerns itself, abstractly, with classifying shapes. You may have heard the joke that topologists can't tell the difference between a mug and a doughnut, or a cow and a sphere: https://en.wikipedia.org/wiki/Spherical_cow#/media/File:Spot_the_cow.gif The machinery behind topology is abstract and involved, but the visual intuition behind it is simple, foreign, and rich. In this class we will be thinking carefully about how different shapes behave and differ from one another, and figuring out some tools to make these distinctions a little bit more precise. We'll hint at several fundamental ideas of topology, i.e. the fundamental group, though we won't go into very much detail. We'll focus instead on why those ideas are important, and how they help us to think about the physical world around us. We'll look at some cool examples—e.g. is it possible to connect each of three houses to each of three utility buildings using pipes without crossing any pipes?—which make for great math party tricks. We'll end looking at a type of shape in space called a 2-manifold: i.e. a shape made out of cloth without edges, like a hollow sphere, or a hollow doughnut. Using the ideas we've built up, we'll figure out ALL of the 2-manifolds.