an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).

The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads.

In mathematics, computational group theory is the study of