An array-structure theory of Maxwell wavefields in affine (3 + 1)-spacetime is presented. The structure is designed to supersede the conventional Gibbs vector calculus and Heaviside vectorial Maxwell equations formulations, deviates from the Einstein view on spacetime as having a metrical structure (with the, non-definite, Lorentz metric), and adheres to the Weyl view where spacetime is conceived as being affine in nature. In the theory, the electric field and source quantities are introduced as one-dimensional arrays and the magnetic field and source quantities as antisymmetrical two-dimensional arrays. Time-convolution and time-correlation field/source reciprocity are discussed, and expressions for the wavefield radiated by sources in an unbounded, homogeneous, isotropic, lossless embedding are derived. These expressions clearly exhibit their structure as convolutions in spacetime. The bookkeeping of the array structure smoothly fits the input requirements of computational software packages. An interesting result of fundamental physical importance is that the ‘magnetic charge’ appears as a completely antisymmetrical three-dimensional array rather than as a number (as in the Dirac quantum theory of the magnetic monopole). The generalization of the array structure to affine (N + 1)-spacetime with N > 3 is straightforward and is conjectured to serve a purpose in theoretical cosmology. No particular ‘orientation’ of the observer's spatial reference frame (like the ‘right-handedness’ in conventional vector calculus) is required.