The goal of this talk is to show that subgroups of free groups are free. We will introduce concepts from algebraic topology following the proof from Reinhold Baer and Friedrich Levi in 1936. We will overview the construction of free groups, the construction of the fundamental group, covering spaces, and linear graphs through definitions and examples. The relation between covering spaces of a ‘nice’ topological space X and subgroups of the fundamental group of X will be highlighted in this talk. Some knowledge of abstract algebra and analysis will be helpful in understanding the material covered.