She did not look out again. The sound of the carriage-springs was no longer audible, the bells could scarcely be heard. The barking of dogs showed the carriage had reached the village, and all that was left was the empty fields all round, the village in front, and he himself isolated and apart from it all, wandering lonely along the deserted highroad. (3.12.15)
After seeing Kitty, Levin feels alone and isolated from the world.
"What can I write?" she thought. "What can I decide upon alone? What do I know? What do I want? What is there I care for?" Again she felt that her soul was beginning to be split in two. She was terrified again at this feeling, and clutched at the first pretext for doing something which might divert her thoughts from herself. "I ought to see Alexey" (so she called Vronsky in her thoughts); "no one but he can tell me what I ought to do. I'll go to Betsy's, perhaps I shall see him there," she said to herself, completely forgetting that when she had told him the day before that she was not going to Princess Tverskaya's, he had said that in that case he should not go either. (3.16.15)
Anna has a hard time making decisions for herself. Maybe this is part of the reason why, later in the novel, Anna has such a difficult time being isolated from society, including Betsy.
Anna pondered for an instant in uncertainty. This shrewd man's flattering words, the naïve, childlike affection shown her by Liza Merkalova, and all the social atmosphere she was used to, – it was all so easy, and what was in store for her was so difficult, that she was for a minute in uncertainty whether to remain, whether to put off a little longer the painful moment of explanation. But remembering what was in store for her alone at home, if she did not come to some decision, remembering that gesture – terrible even in memory – when she had clutched her hair in both hands – she said good-bye and went away. (3.18.34)
Anna exists comfortably among the fashionable, but the memory of her madness when alone goads her into leaving for her meeting with Vronsky.
The attachment he felt to Anna precluded in his heart every need of intimate relations with others. And now among all his acquaintances he had not one friend. He had plenty of so-called connections, but no friendships. Alexey Alexandrovitch had plenty of people whom he could invite to dinner, to whose sympathy he could appeal in any public affair he was concerned about, whose interest he could reckon upon for anyone he wished to help, with whom he could candidly discuss other people's business and affairs of state. But his relations with these people were confined to one clearly defined channel, and had a certain routine from which it was impossible to depart. There was one man, a comrade of his at the university, with whom he had made friends later, and with whom he could have spoken of a personal sorrow; but this friend had a post in the Department of Education in a remote part of Russia. Of the people in Petersburg the most intimate and most possible were his chief secretary and his doctor. (5.21.10)
Without Anna, Karenin is truly alone. Here he realizes that he has no emotional connections with people. By the end of the novel, though, he does have some people whom he loves: his son and Anna's daughter, Annie.
As intensely as Anna had longed to see her son, and long as she had been thinking of it and preparing herself for it, she had not in the least expected that seeing him would affect her so deeply. On getting back to her lonely rooms in the hotel she could not for a long while understand why she was there. "Yes, it's all over, and I am again alone," she said to herself, and without taking off her hat she sat down in a low chair by the hearth. Fixing her eyes on a bronze clock standing on a table between the windows, she tried to think. (5.31.1)
In the hours following her reunion with her son Seryozha, Anna feels more alone than ever. Before meeting Vronsky, Seryozha was the most important person in Anna's life, and now she is separated from him. For more on Anna's relationship with Seryozha, check out her "Character Analysis."
Vronsky could not understand exactly what had passed between the Kartasovs and Anna, but he saw that something humiliating for Anna had happened. He knew this both from what he had seen, and most of all from the face of Anna, who, he could see, was taxing every nerve to carry through the part she had taken up. And in maintaining this attitude of external composure she was completely successful. Anyone who did not know her and her circle, who had not heard all the utterances of the women expressive of commiseration, indignation, and amazement, that she should show herself in society, and show herself so conspicuously with her lace and her beauty, would have admired the serenity and loveliness of this woman without a suspicion that she was undergoing the sensations of a man in the stocks. (5.33.33)
Despite outward composure, Anna is alone and defenseless in the face of Moscow's grandest society. As a result of her public affair, she's a complete outcast. The society women in particular are "amazed" and "indignant" that Anna is showing herself in public. Anna is now isolated from everyone but Vronsky.
Levin did not care to eat, and he was not smoking; he did not want to join his own friends, that is Sergey Ivanovitch, Stepan Arkadyevitch, Sviazhsky and the rest, because Vronsky in his equerry's uniform was standing with them in eager conversation. Levin had seen him already at the meeting on the previous day, and he had studiously avoided him, not caring to greet him. He went to the window and sat down, scanning the groups, and listening to what was being said around him. He felt depressed, especially because everyone else was, as he saw, eager, anxious, and interested, and he alone, with an old, toothless little man with mumbling lips wearing a naval uniform, sitting beside him, had no interest in it and nothing to do. (6.29.2)
Levin is practically the only one who doesn't have a strong interest in how the elections are proceeding; this is yet another way he sets himself apart from the social norm.
"What does he keep reading philosophy of some sort for all this year?" she wondered. "If it's all written in those books, he can understand them. If it's all wrong, why does he read them? He says himself that he would like to believe. Then why is it he doesn't believe? Surely from his thinking so much? And he thinks so much from being solitary. He's always alone, alone. He can't talk about it all to us. I fancy he'll be glad of these visitors, especially Katavasov. He likes discussions with them," she thought, and passed instantly to the consideration of where it would be more convenient to put Katavasov, to sleep alone or to share Sergey Ivanovitch's room. (8.7.6)
Kitty instinctively understands that her husband's preoccupation with philosophy is not helping resolve his existential dilemma. She fears that he's not learning anything by isolating himself from other people.
"No, I'd better not speak of it," he thought, when she had gone in before him. "It is a secret for me alone, of vital importance for me, and not to be put into words. (8.19.13)
When Levin finally achieves spiritual peace, he consciously makes the decision to keep his happiness to himself and not to share it with his wife. Check out Levin's "Character Analysis" for more on Levin's personal epiphany.