Topological graph theory is a way of looking at the structure of shapes. It looks at how the parts of a shape connect to each other, like pieces of a jigsaw puzzle. It's like having a map of all the pieces and seeing how each piece fits together to make the whole shape. In topological graph theory, shapes are made from pieces that can be linked together like dots or lines that form a path between the pieces. This path creates the structure of the shape. By looking at the structure of these paths, we can understand the relationships between the pieces of a shape.