Revenge

Tolstoy uses the following epigraph at the beginning of the novel:  "Vengeance is mine; I will repay," taken from Dueteronomy 32:35.   Tolstoy signifies that he will explore not only man's actions but also man's motives behind those actions.  Alexei has refused to grant Anna a divorce, despite her declaration that she loves another man.  One issue is pride; Alexei has a reputation he wants to uphold.  He does not want his name scandalized by a divorce.  His pride plays such a significant role that Alexei does not actually care if Anna has an affair with another man, as long as the affair remains hidden from public view.  Alexei values his pride more than his love for his wife.  The passion that Anna seeks is lacking, as he refuses to fight a duel with Vronsky.  Anna at one point even wishes he would kill her and show a little passion, so that she could at least respect him.  Unfortunately, Alexei is passionate about, not his love for his wife, but his image. 

Nevertheless, Alexei does show passion in his desire for revenge.  He wants Anna to return to him but not without consequences.

The feeling of jealousy, which had tortured him during the period of uncertainty, had passed away at the instant when the tooth had been with agony extracted by his wife's words. But that feeling had been replaced by another, the desire, not merely that she should not be triumphant, but that she should get due punishment for her crime. He did not acknowledge this feeling, but at the bottom of his heart he longed for her to suffer for having destroyed his peace of mind—his honor. And going once again over the conditions inseparable from a duel, a divorce, a separation, and once again rejecting them, Alexei Alexandrovitch felt convinced that there was only one solution,—to keep her with him, concealing what had happened from the world, and using every measure in his power to break off the intrigue, and still more—though this he did not admit to himself—to punish her (Part 3, Ch. 13).

Not longer jealous, Alexei has progressed to vengeful.  A restoration of the family unit is not enough for him.  Anna needs to understand the enormity of her actions.  His lust for revenge is comparable to her lust for passion, though her lust is forgivable in that she tried to fulfill it in the context of marriage before pursuing the affair with Vronsky.  Alexei wants to see Anna suffer, showing he has no understanding of the internal struggle that led to the affair.  Alexei is an exterior person, and as long as the exterior appears good, the interior is unimportant.  Alexei is unable to see his own motive in wanting to see her suffer because his vision only allows him to view the surface actions, without penetrating further.

Nevertheless, Tolstoy establishes early on that revenge is not for the human scope but God's.  Though human nature craves suffering for wrongs inflicted, man does not decide another's punishment.  So what is man's responsibility?  Forgiveness.  Alexei's desire for revenge and his inability to forgive Anna ultimately plays a significant role in her downfall.