[castle-bravo]

You don't need bandgaps to understand why conductors (other than thin films of ITO) don't transmit light. You derive it from Maxwell's equations and the fact that in a conductor, current density = conductivity * electric field. Griffiths' Introduction to Electrodynamics is the standard undergraduate textbook on electromagnetism, and explains this reasonably well. For bandgaps, Ashcroft and Mermin's Introduction to Solid State Physics is what I'm reading from right now, but you don't need it to understand why metals (conductors) don't transmit light.

[Confusion]

Ashcroft and Mermin is only an 'introduction' in the graduate student sense of 'introduction'. I don't think you can make sense of it without previous grounding in both quantum mechanics and solid state physics.

[castle-bravo]

Well, he did ask about band gaps. Is there a way to understand band gaps without quantum mechanics? I think you only need a little Fourier analysis to get the basics of band gaps.

Anyway, that text and along with Kittel's are the references for an undergraduate solid state course that I'm taking. No prior exposure to solid state physics for me and only introductory quantum mechanics (first half of Griffiths' QM); I find the text totally approachable.