This course is meant to be a *friendly* introduction to the Topology of surfaces. Imagine that you're an ant walking on surface, how would you be able to tell what kind of surface you're walking on? Locally, everything may look flat for the ant, but is the entire space flat? Even if the ant were walking on a ball, it could probably not tell that the surface curves if the ball is large enough. After all, our own Earth locally *looks* flat, even though it's a sphere. In the ant's case, Geometry is not enough for it to know about the world it lives in. This is why we study Topology. In this course, we will learn topological ways to discover how surfaces are different from another.