The Development of Algebraic Structures During the Nineteenth Century

I remember entering the faculty lounge one day while I was in graduate school and hearing a logician chiding some of the algebraists in the room. He said, Don\u27t you fellows ever get tired of just plus and times? His remark, said in jest, had more to it than he may have realized. The fact that there is structure to algebra, represented by plus and times, was a vital discovery in the nineteenth century. It would lead algebra away from a reliance on numbers to a much more formal approach, one in which many different types of algebraic structures could be formed and studied. Algebra would also become more closely allied with other areas of mathematics--hence the liberation of algebra. Our purpose here is to briefly touch on several important advances in algebra during this period and to give a brief overview of some important events in the rise of group theory