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Abstract
In most introductory abstract algebra courses the topics covered are groups, rings and fields. In recent years, semigroups have been included due to their value in certain areas of computer science. However, after a few examples of familiar semigroups, the subject is forgotten and concentration is placed on developing the group structure. In this paper we attempt to show how one could continue examination of semigroups in conjunction with the development of groups. Since the group structure is such a rich and useful one, it would be natural to explore semigroups which are, in some sense, close to groups. The class of inverse semigroups fits this description.