_____The narrator finally makes the break with Gilberte -- after selling his Aunt Léonie's Chinese vase for ten thousand francs so he can send Gilberte flowers every day -- when he sees her walking down the street "with a young man in the twilight." (Actually, he says he "thought" he saw her -- few things happen definitively to our narrator.) He is "now determined never to see her again," and he spends the money so he can "lie weeping in the arms of other women, whom I did not love."
And then there's a bit of foreshadowing:
On one occasion there was an unpleasant scene at home because I declined to accompany my father to an official function, at which M. and Mme Bontemps were to be present with their niece Albertine, who was then little more than a child. The different periods of our life overlap. Because you are now in love with someone who will one day mean nothing to you, you refuse out of hand to meet someone who means nothing to you now, but whom you will one day come to love, someone whom you might have loved sooner if you had agreed to an earlier meeting, who might have curtailed your present sufferings (before replacing them, of course, with others).He also tells us that "all the diverse modes of sorrow will be described in connection with a later love affair." The reader is left to decide whether to take that as a threat or a promise.
But for now he is beginning to experience "the peace of mind of lasting sadness." His imagination dwells on things that might have been, "sweet and constantly regenerated images" that "came to occupy more space in my mind than the glimpse of her with the young man, which weakened for lack of nourishment." He stops visiting Mme. Swann's because "the memory of Gilberte was inseparable from such visits," though he and Gilberte continue to write letters to each other. Hers "were fully as considerate as any I wrote to people who meant nothing to me."
As they slowly grow apart, he begins to regret having decided against a diplomatic career -- a choice he made "so as not to absent myself from a girl whom I would not now be seeing again, whom I had already more or less forgotten." He resumes his visits to Mme. Swann's, which "now caused me no grief at all," but to avoid seeing Gilberte, he more often meets Odette (and her entourage that includes Swann and other men) on her Sunday morning walk. His fascination with Odette is such that he continues to notice the minutest hidden details of her dress, "like the fine Gothic stonework hidden eighty feet up a cathedral, on the corner face of a balustrade, just as perfectly executed as the bas-relief statues in the main doorway, but which no one had ever set eyes on until an artist on a chance visit to the city asked to be allowed to climb up there."
He pinpoints the Swanns' niche in society: "though existing apart from the society of the rich, it was of course a moneyed class, but one in which money had become tractable and had taken to responding to artistic idea and purposes -- in was malleable money, poetically refined money, money with a smile." And he witnesses the Prince de Sagan's attention to Odette as "homage to Woman, even though she was embodied in a woman whom his mother or sister would never stoop to frequent."
And so, at the end of the section "At Mme Swann's," the narrator reports that "the heartbreak I suffered at that time because of Gilberte has faded forever, and has been outlived by the pleasure I derive, whenever I want to read off from a sundial of remembrance the minutes between a quarter past twelve and one o'clock on a fine day in May, from a glimpse of myself chatting with Mme Swann, sharing her sunshade as though standing with her in the pale glow of an arbor of wisteria."