What is the official teaching of the Catholic Church on same-sex marriage?

The Catholic Church's official teaching on marriage is that it is between one man and one woman for the purposes of cooperating with the Creator's work, the good of the spouses, the transmission of life, and the procreation and education of offspring. See the Catechism of the Catholic Church, paragraphs 372, 1534, 1660, 1604-05, 1652-53, 2366, 2363. As all of these basic purposes of marriage cannot be fulfilled, and, in fact, are harmed greatly, by the concept of "same-sex marriage", the official teaching of the Church is that there is no such thing, and that any attempts at supporting it involve mortal sin. Also, please see John Paul II's, Man and Woman He Created Them A Theology of the Body.