There are several themes that carry throughout the novel (and which have been also used effectively in the Broadway musical version) that are enduring and reflect not only the society at the time the piece is set but also are equally appropriate reflections of the modern world. This is one of the reasons that the piece has had such an enduring popularity.
The first is the element of appearance as a "mask" for reality. People are not always as they appear. Of course, Erik is the example that comes most easily to mind. He hides his disfigured face behind a mask, he moves in and out of the hidden underground corridors using his knowledge of them to craft the illusion that he is a "phantom" as well as to take that illusion one step further to appear to Christine as her "Spirit of Music" when she is most ready to believe in him. But Erik is not the only examplee. The opera itself, and theatre as a whole, is a place of illusions. Actors take on roles, and what seems to be magic is really the technical expertise of stage hands and designers. We are transported as audience into a world of illusion, and the novel, in taking us behind the scenes, allows us to see behind the mask of that illusion. Appearance is not always reality.
Another theme is that of innocence. Christine's naivety is what makes it so easy for her to fall for Erik's rhetoric. She also stands in counterpoint to Erik, who has been rejected by the world because he is disfigured. This really ties back into appearance and reality, to an extent. Because of his appearance, he has been rejected which, by extension, has made him become the monster that people viewed him as from the start. We make assumptions, judgements, about people because of their looks. Christine is young and beautiful, so she must be good. Erik is scarred and disfigured o he must be evil. And, in the end, this sometimes becomes a self-fulfilling prophesy. Erik had no other place in society where he could become powerful than the role that he chose. This raises the question of what is our greatest influence - ourselves or the society in which we live. A common theme in literature is the exploration of what it means to be the "other" or that which is not the norm. Erik is different, and it is his difference that causes him to be rejected, scorned, and even feared by society.
Erik and Christine also serve as thematic counterparts in terms of the way in which childhood has shaped them as adults. Erik is longing to experience the kind of childhood that Christine must have had, so he sees in her a surrogate mother. This is evidenced in the fact that the room he has for her is a carbon copy of the room that his mother lived in when Erik was a child. Christine, in wanting to return to the happiness of her own childhood, sees in Erik that Spirit of Music her father had promised her, and she longs to believe in him. He becomes a replacement of sorts for the father that has been lost. Psychologically, this is a reflection on the connections that are created between parents and their children. For Christine, that was one of a loving and healthy relationship that she longed to have back. For Erik, it was one of rejection - even his mother rejected him - and he was looking to experience something that he had never had. In the end, as he releases her from captivity, she releases him through her acceptance of him. The fair maiden has tamed the monster - another common theme of literature wherein innocence triumphs over evil.