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A great deal of what systems engineers do is rooted firmly in the concepts of modern algebra. Despite this fact, however, systems manipulations have often been carried out with little or no awareness of their basic algebraic nature. However, recent years have witnessed a growing cognizance of the intrinsic presence of algebra in systems theory, and this recognition has led not just to further understanding of problems already solved but to unforeseen solutions of problems unsolved by the older, less formal methods. This paper is intended to introduce the art of recognizing the sorts of issues which may be clarified and resolved through the application of modern algebra. Among the topics discussed are modules, quotients, and tensors, together with illustrative applications.