Ok! That seems to be slightly more up my alley, and the group theory would definitely help if I end up taking QFT in grad school (still waiting on decisions, fingers crossed). Something like that but without the hand-waving?The book by Singer "Symmetry in Mechanics" tries to introduce symmetries in the manifold setting but in a way that doesn't assume much math (she doesn't properly define topological manifolds and is pretty hand wavy on lie groups and lie algebras and group actions and their orbits even though she then uses these concepts to talk about conserved systems) however, as noted, the lack of mathematical rigor will leave you unsatisfied and/or confused in my experience.
I can deal with rigor, I just don't want something that requires proving every important non-trivial theorem to finish it. Like I said it's for self-learning and fun, not for reference/a rigorous course.