  Free groups have many applications in Algebraic Topology. In this paper I
specifically study the finitely generated free groups by using the covering
spaces and fundamental groups. By the Van Kampen's theorem, we have a famous
fact that the fundamental group of a wedge sum of circles is a free group.
Therefore, to study free groups, we could try to figure out the covering spaces
of the wedge sum of circles. And in the appendix B, I prove the
Nielsen-Schreier theorem which I will use this to study finitely index
subgroups of a finitely generated free group.
