The Catholic Church still teaches the Ten Commandments. See the Catechism: Part Three, Section Two is enormous1. However, there is a helpful summary:
2075 "What good deed must I do, to have eternal life?" — "If you would enter into life, keep the commandments" (Mt 19:16–17).
2076 By his life and by his preaching Jesus attested to the permanent validity of the Decalogue.
2077 The gift of the Decalogue is bestowed from within the covenant concluded by God with his people. God's commandments take on their true meaning in and through this covenant.
2078 In fidelity to Scripture and in conformity with Jesus' example, the tradition of the Church has always acknowledged the primordial importance and significance of the Decalogue.
2079 The Decalogue forms an organic unity in which each "word" or "commandment" refers to all the others taken together. To transgress one commandment is to infringe the whole Law (cf Jas 2:10-11).
2080 The Decalogue contains a privileged expression of the natural law. It is made known to us by divine revelation and by human reason.
2081 The Ten Commandments, in their fundamental content, state grave obligations. However, obedience to these precepts also implies obligations in matter which is, in itself, light.
2082 What God commands he makes possible by his grace.
1 "Your questions should be reasonably scoped. If you can imagine an entire book that answers your question, you’re asking too much." [Link]