Topological geometry is a type of math that is used to study the shapes of things. The way it works is by looking at all the different ways things can be connected together, like the way pieces of a jigsaw puzzle fit together. For example, if you have a square and a triangle and want to put them together in the same way the pieces of a puzzle fit together, topological geometry can help you figure out what kinds of shapes you should make and how everything can fit together.