This thesis aims at giving a brief survey of a few of the algebraic, geometric, and topological techniques used in developing the theory of $Out(F_n)$, the outer automorphism group of the free group on $n$ generators. Much of the study of $Out(F_n)$ has been developed through analogies and connections with mapping class groups and general linear groups. Throughout this paper, we will repeatedly ... read morediscuss the evolution of methods for $Out(F_n)$ in regards to their analogous counterparts in the setting of mapping class groups and general linear groups.
