Thanks for the response. But in fact, the problem is precisely that Mail is opening 17 main windows. Yes, MAIN windows. I know it isn't supposed to have this functionality, which is what makes this so bizarre. But I have 17 main windows that can be maximized or minimized at any moment.
However, your answer has inadvertently solved my problem. I just tried closing each of the windows individually before shutting down the program. When I re-opened it after doing that, only one window opened. So, it seems as though the problem is solved for the moment. But the fact that it did this in the first place is a bit disconcerting as it seems like a drastic step outside of what Mail is supposed to do, which suggests a major glitch, or perhaps even a virus...