Much in the early Christianity is modelled after the Jewish customs and what is written in the Old testament.
1. The moral laws and the laws agains idolatry remain valid
2. Instead of the sacrifices of animals we have the Eucharist
3. Tithes are owed not to the priests in the old Temple but to the prophets (today those are the monks), to the bishop and to the poor (according to the Didache)
4. The festivals are modified so that they become clearly distinctive from the Jewish festivals (the Christians have Passover/Easter but it is celebrated in a different day)
5. Also Sunday instead of Saturday
6. Deacons/Presbyters/Bishops correspond to Levites/Priests/High Priest.
But what about the dietary laws of the Torah? Such laws are not exactly laws about ritual. To the nations who don't eat pigs (the Jews including) the pigs are repulsive so to the Judeochristians it wasn't obvious that the dietary laws are not ethical laws. And this was the source of a the controversy in the early Church. The Didache tries to reconcile the arguing parties. According to it, it wasn't necessary to follow the dietary laws of the Torah, it was, however, a good thing to do so.