We recall the definition of the fundamental group develop in the previous lecture then prove that it is indeed a group. Finally, we show that the fundamental group of the circle is isomorphic to Z, the integers.

We give a quick review of group theory then discuss homotopy of paths building up to the definition of the fundamental group.

When are two shapes the “same”? Topics covered include deformation retract, homotopy of maps, and the homotopy equivalence of spaces.