Are free groups abelian?

Could you please elaborate on the concept of "free groups" and "abelian groups" and explain why the question "Are free groups abelian?" arises in the context of algebra and group theory? Are there specific properties of free groups and abelian groups that lead to this inquiry, and if so, what are they? Additionally, could you provide a concise yet comprehensive answer to the question, considering the fundamental definitions and properties of these groups?