What is the central idea or theme of The Phantom of the Opera by Gaston Leroux?

Appearance versus reality is the central theme, as has been mentioned by the previous answers. Nothing is what it seems in The Phantom of the Opera. The Phantom deceives Christine by claiming he is an angel sent from her deceased father when in truth he is a human man living beneath the opera, trying to claim Christine for himself. Christine appears to Raoul to be a faithless coquette when in reality she is under the Phantom's influence and terrified out of her mind.
Ambition and its costs are a smaller theme. Christine's success in the opera comes from having her voice trained by the Phantom as well as his threats to the management. However, in exchange for her success, the Phantom demands both her love and for her to dissolve her entire social life. Her own selling of her freedom can be seen as a parallel to the Faust opera the company puts on, where a man sells his soul to the devil in exchange for power and youth.

There are several major themes in The Phantom of the Opera. Perhaps the most important one is that of appearance versus reality. The very setting of the story, which is focused around the performance of opera, emphasizes this contrast. On one level, we have the theatrical illusion of singers and dancers creating a vision of stories about imaginary people, often in exotic settings. On another level, the novel goes backstage to reveal the details of how the operatic illusion is created. Erik himself is a master of illusion, including such skills as ventriloquism. His character, though, with the facial deformity that makes him appear almost death-like and the mask he wears to conceal it, suggest an uglier element of illusion, namely the way in which society conceals disability.
A second theme that drives the plot is the power of love. While the main romance is that of Raoul de Chagny's love for Christine, Erik is also motivated by his desire for her, and both his evil deeds and his eventual redemption are both motivated by that.

One of the primary themes of The Phantom of the Opera is the difference between appearance and reality, as well as what can happen when people fail to understand that difference. This is most seen in the character of Erik, the Phantom, but it applies on multiple levels even within his character. When Erik does not show his full face, he goes around masked and uses illusions to make himself seem like a "phantom." In this guise, he appears alternately terrifying—to the people at the opera house—and alluring—to his student, Christine. He seems elegant and sophisticated to others, which contrasts his dank, grim lifestyle and the harsh words with which he expresses his true feelings about humanity. Erik also uses Christine as a vehicle for illusion when he becomes her "Spirit of Music" and secretly helps her.
On the other hand, Erik is the way he is because he was rejected for his looks. He might have been a kind and loving person, but he was treated as a monster because of his appearance, and he has ultimately succumbed and become a monster himself. In this, the danger of "judging a book by its cover" is shown. Erik is, indeed, brilliant and sophisticated; what might he have been had he been treated better as a child and not shunned?