Ahh, this is the core of the matter. I have long been familiar with the graphic image of the magnetic field propagating through space as a sine wave, with the electric field propagating along the same line but polarized at a right angle to the magnetic field. What I was really wondering is, what exactly is the medium through which the wave propagates? Because, as we all know, our conventional understand of waves and energy require that you can't have a wave formed of nothing; the wave is a traveling oscillation jostling gas (or other) molecules around, in the case of sound; or a mobile inequity in the depth of a body of water, in the case of surf.
Apparently, with electromagnetic waves it's some sort of transmissible inequity allowing energy to be stored and released sequentially, in a process that propagates at rate c, in space itself.
I'll have to look up that book.
Waves propagate by changes in the strength of fields over time. Fields change their strengths because of changes in the state(s) of the particles that generate the fields. To go deeper requires consideration of the meanings of concepts such as space-time, mass and energy. At that level, thought and communication become rather difficult, because analogies and metaphors with common experience become problematical, to say the least. Our culture, language, semantic models and perhaps even our very brains are not designed for it. We are lucky when we finds ways to model such things using some formalism (e.g., mathematical equations.) We are even luckier when the meaning of such formal models can be translated into common natural language.
There is no medium, or really no external medium. In short a time varying magnetic field results in an electic field, also time varying. But a time varying electric field also results in a time varying magnetic field. The "wave", which need NOT be sinusoidal, just sort of pulls itself along by it's bootstraps, so to speak. (that might not be a very good description, but it's about as good as it gets without the math). Sinusoidal is the easiest and most common solution to Maxwell's Equations, but not the only one. They come in several forms, see Maxwell's Equations all of which are equivalent. My favorite version of the equations, usually the most general version, either of the two forms shown at the link above, above which is written, "And God said:" and below which is written. "And there was light!" :)
The death knoll of the "ether" theory of electomagnetic propagaton was the Michaelson-Morely experiments, which in turn led to Einstein's special theory of relativity, and the famous E=MC^2. The "ether" was the postulatd medium for the propagation of light and other EM waves.