The fundamental Group of the Torus is abelian

This video illustrates the proof of the Theorem in the title. The proof goes like this: Consider a rectangle. Then the path going up the left side of the rectangle and then along the top is homeomorphic to the path going first along the bottom and then up the right side. Gluing the rectancle to make a torus, this shows that going first around through the hole and then along the outside is homeomorphic to going first along the outside and then through the hole.