The Court’s 2017 Advisory Opinion on same-sex marriage is now available in English.

I/A Court H.R., Gender identity, and equality and non-discrimination with regard to same-sex couples. State obligations in relation to change of name, gender identity, and rights deriving from a relationship between same-sex couples (interpretation and scope of Articles 1(1), 3, 7, 11(2), 13, 17, 18 and 24, in relation to Article 1, of the American Convention on Human Rights). Advisory Opinion OC-24/17 of November 24, 2017. Series A No. 24.

http://www.corteidh.or.cr/docs/opiniones/seriea_24_eng.pdf