The individual versus society
Society in The Age of Innocence is a powerful force that demands that individuals sacrifice themselves to its forms and conventions. Often, the chief mouthpiece for society is the family - in particular, those old money families that dominate New York society.
Archer wants desperately to be with Ellen, but society would not approve such a choice. When he decides to follow Ellen to Europe, May reveals that she is pregnant, and he knows that this turn of events seals his fate. Finally, he cannot muster the determination to go against the mores of his world.
Ellen wants to divorce her husband and be free, but Archer persuades her that she will hurt her family and be censured by society. Her family even wants her to go back to the husband who mistreated her in order to uphold society's values, and they cut off her allowance when she refuses. After a heroic attempt to change herself and fit into New York society, she gives up and returns to Europe, though not to her husband. Her defeat is completed by May's announcement to her that she is pregnant: society upholds a man who sticks by his wife and baby, and abhors one who abandons them.
Archer is instrumental in teaching Ellen to deny her own wish to be with him for others' sake, though ironically, he does not wholly believe that this is the right thing to do - it is simply what the family and society wants. But she takes Archer's lesson to heart because she believes it is a finer and more unselfish way to live than she has known in her past.
In the end, Ellen reasserts her individuality by leaving America, though at great cost: she is forced out of New York society by the "tribe" of the family, who assume that she is having an affair with Archer. She gives up Archer and her family to regain some degree of freedom and individuality in Europe. Archer remains within the world he knows so well, though as with Ellen, he pays a price: he feels he has missed "the flower of life." On the other hand, he has preserved his family intact, has led a contented life, and is respected within society.
Appearance versus reality
New York society values correct appearances more than reality. People know that Beaufort conducted illicit business deals, but overlook them as long as they are not the topic of general gossip. Lefferts pronounces on other people's morals at the same time as he is having extra-marital affairs. May and Archer know that Ellen does not come to the ball where they announce their engagement because she wants to avoid bringing shame on the family, but May pretends, even to the man she will marry, that it is because she lacks a suitable dress. Archer, at this point, admires May's ability to avoid unpleasantness. He comes to despise this quality in her, but this is the man who, when given his second chance to be with Ellen, is concerned about how he will appear to society. In the end, Archer admires and respects May's supreme achievement in managing appearances, when he learns that in spite of her apparent conviction in the perfect harmony of her household, she knew about his feelings for Ellen and that he had sacrificed them for her and the family.
The consequences of society's focus on the superficial can be serious. It hardly matters that Ellen and Archer do not act on their love. Society assumes that they are having an affair and expels Ellen.
New society versus old society
Old New York society is exemplified by May Welland, the demure, traditional girl from an 'old money' family who is devoted to her husband and who is concerned always to do the correct thing. May's family (with the exceptions of Ellen and the fiery old Mrs Mingott) act in solidarity to promulgate the accepted social codes. This society, with its rigid conventions, is challenged by the arrival of brash new incomers like the Beauforts and Ellen Olenska. Beaufort borrows some respectability from his wife, a member of an 'old money' family, and throws lavish parties, so society tolerates him for a time despite being aware of shady deals in his past. But when his illegal dealings become public knowledge, the old New York society can only expel him and his wife and pretend they never existed. Ellen also fails to integrate into this old society - she simply too "different."
The extent to which old society has become defunct and a new order taken over is shown at the novel's end by the change in attitudes to people like the Beauforts. Society now values different things - new ideas and movements, amusing or artistic people. Dallas Archer is to marry Fanny, Beaufort's illegitimate daughter, and not only does the new society not object, it values Fanny for her lively personality. There are no societal obstacles remaining to Archer's and Ellen's relationship, either, though Archer is too stuck in the old ways to take advantage of the change.