[graycat]

Group theory is a standard topic in a college course, say, at the junior level, in 'abstract algebra'. So, the other topics typically are rings, fields, vector spaces, maybe the construction of the rationals and reals. The course might also toss in a little on number theory.

Anyone with a ugrad pure math major is supposed to know what a group is and the early, standard theorems.

Group theory was used by E. Wigner for the quantum mechanics of molecular spectroscopy so that at times some chemistry students want to know some of group theory and group representations.

My ugrad honors paper was on group theory.

I published a paper showing how a group of measure preserving transformations could lead to a statistical hypothesis test useful for 'zero-day' monitoring for anomalies in server farms and networks.

Group theory pops up occasionally. Get a good, standard text in abstract algebra or two or three and spend a few evenings. If you get to Sylow's theorem, you are likely deep enough for starters. Group theory is very clean, polished stuff and can be fun. Go for it.