Mathematics is a creative process, and unfortunately, that process is often hidden from students of the discipline. This is certainly the case in the area of mathematics commonly referred to as abstract algebra. Current pedagogy conceals from the student many of the great ideas generated by significant problems in the history of the discipline. In his famous paper "Memoirs on the Conditions for Solvability of Equations by Radicals" [1, Appendix 1], Evariste Galois introduced the mathematical term "group" and identified a specific property of groups, now known as "solvability", which enabled him to translate his original problem from the theory of equations into an equivalent problem within the newly established theory of groups. This article will explore Galois' definitions of "group," "conjugate group," "normal subgroup," and "solvable group" and suggest how they can be used to enhance the learning of students as they encounter these concepts in a first course in abstract algebra.