This first volume of this two-volume set deals with the important recent discovery of the photomagneton of electromagnetic radiation, a discovery which is fundamental in quantum field theory and in quantum mechanics in matter. The photomagneton is the elementary quantum of magnetic flux density carried by the individual photon in free space, and is generated directly by the intrinsic angular momentum of the free photon. The volume develops the theory of the photomagneton in a series of papers, which cover all the major aspects of the theory, from classical electrodynamics to the relativistic quantum field. Several suggestions are given for experimental tests, and the available experimental evidence is discussed in detail. The overall conclusion of the series of papers is that the photomagneton, which is observable experimentally in magneto-optical phenomena, indicates the presence in free space of a novel, longitudinal, magnetic flux density, linked ineluctably to the usual transverse components. If the photomagneton is not observed, then a paradox would have emerged at the most fundamental electrodynamical level, necessitating a modification of the Maxwell equations themselves.