Well, Monster is really a pretty serious show. The plot here really shines. It's essentially a mystery, with some rather mystical-seeming things mixed in. However, it all keeps very true to reality, and there's no magic, metaphysics, or mecha involved anywhere. Excellent European flavour.
some spoilers for the couple of eps ahead - but don't worry, that's not even a tiny fraction of the real plot involved. Read on.
Basically, it starts in 1986 in Dusseldorf, Germany. Dr. Tenma, a Japanese brain surgeon who moved to Germany to study, and then work there, works at Eisler Memorial Hospital, where he is looked up to as a prodigy, a doctor of incredible talent. This is why the most famous, important patients are always brought to his care - order of the hospital's Director.
However, one day a Turkish worker injured in an accident dies while Tenma works on a famous opera singer, by the order of the director - even though the Turkish man was brought in first. The image of the worker's grieving wife haunts Tenma, and next time this happens, he disobeys on the Director's order and operates on a boy who was shot in the head, instead of the city mayor who was brought in! The boy was found in a house, with his parents - officials who recently escaped from East Germany - dead, and his twin sister in shock.
The mayor dies. Now, Tenma gets on the unfavourable side of the Director, and his hopes of promotion fade away. His engagement to the director's daughter is off, and all seems to be lost...
...however, the boy and his sister mysteriously disappear. The same night, the Director and two of his newly-favorite doctors are found dead.
What will happen to Tenma now that his corrupt superior is dead? Will he be suspected of the murder? And more importantly, how is this related to the mysterious twins?
The answers will not be found for another 10 years, when Tenma meets his patient again...