What does Jewish law tell us about animal sacrifices?
Sacrifice of animals dates back to earliest times; it was practiced, for example, by Abel (Gen.4:4) and Noah (Gen.8:20). The Jewish sacrificial laws are detailed in the first seven chapters of Leviticus. These laws were in effect until the Second Temple was destroyed by the Romans in 70 C.E. They are no longer operative because, ever since the Temple was first built by Solomon (1 Kings 5ff), sacrifice outside the Temple has not been permitted (see, e.g., Lev. 17:1-7).
G-d found the sacrifices of both Abel and Noah appropriate, but as the Bible tell us repeatedly G-d wants righteousness and repentance, not sacrifice. Verses on this topic include 1 Samuel 15:22, Psalms 51:17, Hosea 6:6, etc. In his Guide for the Perplexed (III:32) Maimonides explains that the Torah requires sacrifices because that was the expected form of worship in those days. One of the Rabbis of the Talmud used to say that fasting, which diminishes a person’s fat and blood, should be even more effective than offering the fat and blood of a sacrifice on the altar (Berachos 17a).