My daughter's almost sixteen and has been enjoying this show recently.
It's mature in the themes that are portrayed, not the portrayals themselves. There's very little sexuality except by reference (a couple of scenes take place in a "red light" district, for instance), and very little of the violence is extreme. Most episodes have no violence at all. People do get shot, beat up, etc., from time to time, but it's not vivid or gory. It's much more of a psychological "mystery/thriller" than a "horror" show.
At your age you might find the underlying issues more difficult, though. A good portion of the story concerns the abuse of children, mostly psychological abuse but some (off-screen) physical abuse as well. Monster also contains many historical references to the former communist regimes in Eastern Europe, particularly East Germany and what was then called Czechoslovakia. Being as old as I am, and being a student of politics, the Cold War was an integral part of my life for about forty years. It has progressively less relevance to folks in your generation, but I don't think that's a reason for not watching the show. I've enjoyed many historical animes that take place in the Heian and Edo periods in Japan, or in fantasy classical Asian societies, and I wasn't alive then, or at least not in the form I have today.
OT: I was going to post this suggestion in your other thread on horror shows. You may think it's too "kiddy" or "girly," but you might want to try
Tweeny Witches. Sadly it just got licensed, though.