A sphere with a handle
The theorem of classification of the surfaces states that any compact, connected, orientable surface without boundary can be related to a standard surface. We can visualize these standard surfaces as spheres with some handles attached. In the figure, we see an example with one handle and it is easy to imagine spheres with a greater number of handles, while the preceeding step with 0 handle is the sphere. Otherwise, another equivalent standard shape is a doughnut with a certain number of holes.