I have never had an advanced classical mechanics class, only elementary level treatments using mostly Newtonian approaches, on very simple mechanical systems. I'm interested in learning about continuum mechanics, having in mind the applications in the applied field of seismology, which studies the propagation of mechanical waves in the solid (and molten) earth. I don't need to see applications in this introductory study. My math background is mostly engineering oriented, only recently did I start some light reading on "modern math" such as abstract algebra, topology and soon, measure, Hilbert space, etc. I can do some simple vector and maybe tensor calculus, but not differential forms. I've seen some ODEs and PDEs and solutions using separation of variables, etc, but never learned any general theorems regarding the existence, uniqueness, etc. I have some experience on classical EM waves and fields and Green's functions, but mechanical waves as I understand are tensor waves, probably harder to get used to. Now where should I start to learn the basics? I don't want a book written for undergraduate engineering students with inadequate math background, in which case the treatment typically tend to become ad hoc and very awkward, but my background won't accommodate a highly rigorous treatment using lots of geometry either, is there anything in between that emphasize more on the theory rather than applications? Thank you for reading these through, if you have any suggestions it is even more appreciated.