There are four main instances in Greek literature where marriage is described, either overtly or as a theme related to other aspects.
In Sophocles' play Antigone, marriage can be said to be the reason for the demise of so many of the lead characters. Although the play centers on Antigone's love for her brother, the result of that love is that when she dies, her husband Haemon also kills himself. In consequence of this, Haemon's mother, Queen Eurydice, becomes distraught over both Antigone and Haemon passing away. In the end, she kills herself too. The king, Creon, suffers immensely as a result of all these deaths. In trying to keep the polis together, he ends up sacrificing those closest to him.
In this story, the theme is of marriage as a bond between families, having consequences for not only the husband and wife but also the people around them. Love can be an intensely destructive force, and marriage is a deep bond tying not only people but also households to one another.
In Homer's poem, Hymn to Demeter, the stages of womanhood are depicted as seasons, and marriage is seen as the reason for the mother entering her final stage. There are four stages, birth, young age, marriage and maternity, and death. When Persephone is stolen by Hades, Demeter loses her motherhood, and Persephone loses her young age, because the two are interdependent. Marriage in this case, for Persephone, is a shouldering of responsibility and moving away from her maternal home. It is the end of youth and the beginning of maternity. But for Demeter it is the beginning of the death, her final stage. Because Demeter was linked to the Earth, the earth sorrowed. So while not directly linked to marriage, the importance of marriage as a stage in a woman's life is seen in this poem.
Another take on marriage is depicted through the writings of Sappho. While she was married and had a daughter, her writings describe a sort of playful idea of love that is expected from a much younger woman. Indeed, her ideas of love might be said to be bisexual, and from her interest in other people around her, it might be surmised that she wasn't quite as content in her marriage as it may seem. Her attraction to women, in particular, can be seen as erotic because it occurred despite her bond to her husband. It adds a female and unconventional voice to the ideas in Greek literature surrounding marriage.
Finally, in the Odyssey, we see marriage as a contract, the failure of which leads to devolvement of the household. When Odysseus is presumed lost and dead, Penelope is faced with many suitors who try to win her hand so that they can gain status in the polis. Her marriage is depicted as a prize that needs to be won for status. Even when Odysseus returns he has to compete to win her hand. Although he wins, because of their special bond, this still shows marriage as something that needs to be achieved in Greek society.