The author maintains that a course in the classical theory of the electromagnetic field, with full exploitation of vector calculus methods, should be thought of as being as much of a basic essential in any physics honours course as is a course on classical mechanics. It is suggested that if the mathematical techniques are taught in a way that relates them directly to the central notions of field theory and avoids discussion of special techniques, the mathematical burden is sufficiently light to be borne by all physics students, not only those theoretically inclined. The course need not be of excessive length if it is understood as exclusively an introduction to field concepts and hence not to cover in any detail the electric and magnetic property of materials. A number of particular ideas arising from the author's teaching experience are discussed.