Mask (Symbol)
Erik's masks -- and he has several -- allow him to pass briefly in human society without being noticed. Yet the mask also sets him apart from other human beings, with whom he does not interact directly. He is therefore alienated from human society despite his ongoing attempt to join it. His own mother would not kiss him, but rather forced him to wear a mask. It is Christine's willingness to take his hand and kiss him on the forehead that breaks through to Erik and inspires him to act with kindness and compassion.
Madness (Motif)
Many people have occasion to question their sanity throughout the book. The credulous Christine at first believes she is hearing her father's "Angel of Music," or perhaps her father himself, although in reality it is Erik. Using his trap-doors to move silently and mysteriously through the Opera-house, Erik plays pranks on the staff and singers, causing them to question their memory. M. de Chagny becomes completely disoriented and confused in the torture-chamber, and Erik himself becomes increasingly unhinged as his obsession with Christine leads him to kidnap and torture the Persian and M. de Chagny. Erik is almost completely delusional near the end of the novel, due partly to the infected bullet wound that eventually claims his life.
Marriage (Allegory)
Erik is obsessed with Christine and wants to marry her, yet he encourages her to pretend to be engaged to Raoul for a month before he leaves on a scientific expedition to the North Pole. Unfortunately, a week into the game Raoul realizes he really is in love with Christine. Throughout their "courtship," Erik supervises them closely.
Erik's fixation with Christine is not simply a matter of physical desire. Although Erik is attracted to Christine physically, sex is not his primary motive for wanting to marry her. What he desires above all else is to be loved, appreciated, and accepted for his own sake. Late in the book, after he releases the Persian narrator and the other men he kidnapped, Erik agrees to take the men to the surface as a favor to his wife. To save Raoul's life, Christine agrees to marry Erik, and in fact she commits emotionally to this decision even though she does not love him. She holds his hand, kisses him on the forehead, and shows him some of the basic human decency he has longed for since childhood. Satisfied emotionally, and feeling accepted and loved for the first time in his life, Erik behaves as though he is already married, and lets the men go as a favor to someone he loves.
Music (Symbol)
Throughout the novel, musical performance is used to symbolize deep spiritual experience. Christine's father told her stories of the "Angel of Music," who appeared to all worthy musicians at some point in their lives to provide divine inspiration. Initially, Christine mistakes Erik for this Angel. Under the Phantom's tutelage, Christine learns how to use her voice more expressively and with a unique tone that causes her to be singled out for a lead role (instead of simply singing in the chorus). In many ways, Erik gives Christine his music: the most intimate gift he has to offer. Yet it is Christine's voice that causes her childhood friend Raoul to remember her fondly and to eventually fall in love with her.
Trap-Doors (Symbol)
Erik is, among other things, a brilliant architect and engineer. He has a system of hidden passageways and trap-doors in the Opera, and can move about the building at will. Having lived in and below the building for years, he has set up a variety of inventions that aren't quite nice. One of them is a booby trap containing enough dynamite to blow up the Opera. Another is a torture chamber consisting of mirrors through which Erik can cause images to reflect so that Raoul and the Persian think they are somewhere else.
Erik has power over the managers of the Opera chiefly because of the trap-doors. Not only can he come and go as he pleases between Box Five and his home on the underground lake, but he can also cause unfortunate "accidents" to occur. This is why the former opera managers paid him a regular allowance: it was easier to pay Erik off than to tolerate his somewhat sociopathic caprices.