Reddit reviews Symmetry: An Introduction to Group Theory and Its Applications (Dover Books on Physics)

J.F. Cornwell, Group theory in physics: an introduction (link)

W. Ludwig, Symmetries in physics: group theory applied to physical problems(link)

M. Tinkham, Group theory and quantum mechanics (link)

W.-K. Tung, Group theory in physics (link)

E.P. Wigner, Group theory and its applications to the quantum mechanics of atomic spectra (link1, link2)

N. Jeevanjee, An Introduction to Tensors and Group Theory for Physicists (link)

G. Costa, Symmetries and Group Theory in Particle Physics: An Introduction to Space-Time and Internal Symmetries (link)

B. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (link)

R. McWeeny, Symmetry: An Introduction to Group Theory and Its Applications (Dover Books on Physics)(link)

Weyl's symmetry is what you're looking for. The next step up from this would require some group theory, since mathematicians interested in symmetry usually study symmetry groups of objects or spaces. I have not read it but this book looks like a good next read, at least the first four(ish) chapters. Another possibility is Armstrong's book, though I'm not familiar with this book either.

This book is a good introduction to group theory and representations. It specifically has sections devoted to crystallographic groups.

I used McWeeny in my graduate Group Theory course. Not sure if there's a pdf floating around, but you can get it for under $10. It was a rather good introduction. Another mentioned Dresselhaus, which I've heard good things from as well.