The phantom symbolizes the contrast between what is real and what isn't. Wearing his mask, he's a man with whom Christine can sympathize. Without his mask, he is so horrible that Christine can no longer look upon him. this can be extended to the mask that we all wear in dealing with others.
The phantom also symbolizes illusion. No one knows if he really exists or not. The phantom's elusive character again represents the appearances that people put on, so others won't know the true reality of their lives.
The opera house represents the dark side of life, the evil that exists in life. If you look at how it's described, it helps the author to create the elements of horror.
Erik's face represents death. As a young man, he billed himself as the living dead man.
These are but a few of the symbols, but if you go to the website below, you can find further details.
The Mask, The Monkey with the symbols, And the Rose with a black ribbon
Based on Sir Andrew Lloyg Webber's adaptation of the novel, it can also be his mask, the rose which he gives to Christine after every performance (in the 2004 movie, the rose had a black ribbon) and his notes or his music.