I have for some months been interested in group theory. I was very fascinated by the level of abstraction I first met when working with groups. Another aspect that has fascinated me lately is symmetry.
I've noticed symmetry in proofs I've written, programs I've made, and often these symmetries strike me as extremely basic but still fundamental.
My question is concerning this "simple symmetry" (for example, the symmetry of electric charge, symmetry in undirected graphs and often symmetry popping up in simple programs that I write).
How can I use knowledge of group theory to better understand these kinds of symmetries? How should I think of them?
Also - I am currently reading some introduction to group theory, but I have to admit that I am not at all as motivated as I used to be. How can I keep up my motivation in studying group theory?
I hope my questions are clear, as you have noticed, I am not experienced in this field nor in mathematics generally, at least not yet.