One important theme of Anna Karenina is announced in its famous opening line:
All happy families are alike; each unhappy family is unhappy in its own way.
Families, and the ways in which family members contribute to each others' happiness or misery, are explored first in the the relationship of the Oblonskys, then among the Rostovs and the Karenins, and in Levin's marriage to Kitty.
Another theme closely related to that of family is forgiveness. Tolstoy shows forgiveness as vital to family life and human life in general and depicts his characters struggling to forgive each other for infidelity and inflicting pain. It is only when they do so that they are able to find peace.