A while back I was learning about finite groups in an algebra class. I mentioned to a friend that finite group theory might be an interesting area of research to pursue. She asked something along the lines of "Isn't finite group theory 'done?' I thought that ended with the classification theorems."
I'm not sure how to answer. Is finite group theory still an active area of research? If so, what are some of the common problems that professors and graduate students are working on right now? Are there any reading materials to get more acquainted with such things?