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Maxwell's equations have undergone several changes of form in the 150 years since they first emerged. This has been due not only to changes in their mathematical expression and physical interpretation, but also to historical accidents and trends. This article examines: what they were in the beginning; how they evolved into their customary form over the course of 40 years; the significant variations there have been since then; who have been the major proponents of these changes; and finally, what they did, or did not, contribute. Brief explanations of the main mathematical variations are included.