Anna Karenina Part 4, Chapters 1-15
"The Karenins, husband and wife, continued living in the same house, met every day, but were complete strangers to one another. Aleksey Aleksandrovich made it a rule to see his wife every day, so that the servants might have no grounds for suppositions, but avoided dining at home. Vronsky was never at Aleksey Aleksandrovich's house, but Anna saw him away from home, and her husband was aware of it." Part 4, Chapter 1, pg. 373
Anna sees Vronsky all the time, with Karenin fully aware of it. His only request is that Vronsky stay away from the house. It seems a minor request, given the situation. Yet Anna manages to violate it, inviting Vronsky to the house one night when Karenin isn't expected at home. Karenin, however, arrives home earlier than expected and meets Vronsky on the front steps. He is enraged inside and tells Anna he will divorce her and have his sister raise the boy.
Shortly after, Anna has an ominous dream, which predicts her forthcoming death. The dream continues to recur throughout the rest of the book.
Meanwhile, Levin and Kitty meet once again at a party thrown by Stiva. Levin realizes that Kitty must love him because of the longing look in her eye. He proposes, using covert signals that she, but no one else, understands.
"Levin got up and escorted Kitty to the door. In their conversation everything had been said; it had been said that she loved him, and that she would tell her father and mother that he would come tomorrow morning." Part 4, Chapter 13, pg. 439
This is an example of the fact that Levin and Kitty relate to each other on a subconscious, intuitive level. They equal harmony, the kind Levin has always been searching for. The same could hardly be said of Anna and Vronsky. Levin finally asks publicly for Kitty to be his wife, and her parents are thrilled. He apologizes to her that he is not a virgin. She forgives him.
Part 4, Chapters 16-23
Karenin gets word that Anna is dying. Through a telegram, she asks him to come see her. At first, he doesn't believe she can be dying. After all, she has lied a thousand times. Still, he needs to see her. Once he gets there, he meets Anna's new illegitimate daughter and finds Anna herself suffering from a high fever. She begs Karenin to forgive her and Vronsky. Karenin does so. This makes Anna feel prepared for her own death.
Meanwhile, Vronsky is embarrassed by the sight of Karenin and tries to commit suicide by shooting himself. His servant finds him in the nick of time, though, and he does not die. Karenin has come in contact with some kind of inner peace for the first time in his life. He even says he will raise Anna and Vronsky's daughter.
Anna begins to bounce back and recover, much to Karenin's surprise. He once again grows angry when he Anna requests to spend time with Vronsky before he leaves for a new job. Karenin is angry with himself for forgiving them, and he calls the divorce off.
Stiva, who is worried about his sister, begs Karenin to give Anna the divorce, and Karenin grudgingly agrees. Betsy goes to tell Vronsky the news. Vronsky is overjoyed that Anna is finally his. The two decide to move to Italy together. Anna refuses Karenin's offer of divorce, because it would deny her custody of Seriozha.
"'Oh, why didn't I die? It would have been better!' she said, and tears flowed silently down both her cheeks; but she tried to smile so as not to hurt him." Part 4, Chapter 23, pg. 457
The threat of death makes Anna remorseful, Karenin forgiving and Vronsky deeply ashamed. Once Anna improves, moods begin to shift again, as Kitty is now pregnant.
"In spite of death, he felt the need for life and love. He felt that love saved him from despair, and that this love, under the threat of despair, had become still stronger and purer. The one mystery of death, still unsolved, had scarcely passed before his eyes, when another mystery had arisen, as insoluble, calling to love and to life. The doctor confirmed his suspicion about Kitty. Her indisposition was pregnancy." Part 4, Chapter 20, pg. 530