We will introduce some necessary basic notions regarding formal languages, before proceeding to give the classification of groups whose word problem is context-free as the virtually free groups (due to Muller and Schupp (1983) together with Dunwoody's accessibility of finitely presented groups (1985) for full generality). Emphasis will be on the group theoretic aspects of the proof, such as Stalling's theorem on ends of groups, accessibility, and geometry of the Cayley graph (rather than emphasizing details of formal languages).
