This blog post isn't exhaustive but I've tried to pick the key or summative passages about the Law.
What’s the purpose of the Law?
- Show Sin: The holiness of God enshrined in the Mosaic Law, "I am Holy" says God. (Lev 11:44-45) The Law was brought into the world so that trespasses might increase (Rom 5:20), it's introduced to show sin (Rom 7:13) “Why, then, was the law given at all? It was added because of transgressions until the Seed to whom the promise referred had come." (Gal 3:19) For lawbreakers and rebels, (1 Tim 1:9) showing us guilty even if we break just one part. (James 2:10)
- Guide Obedience: Those who follow God will obey the Law. (Lev 18:5) Jesus says “If you want to enter life, keep the commandments.”(Matt 19:17) "Keeping God’s commands is what counts.” (2 Cor 7:19) All Scripture including the Law is "useful for teaching, rebuking, correcting and training in righteousness." (2 Tim 3:16)
- To Shape our worldview: God gave ancient Israel the Law so that other nations may see his glory. (Deut 4:5-8) Jesus points to the two-fold summary of the Law as the essence of obedience. (Matt 22:40) Jesus rebukes the Pharisees for thinking that mere obedience is sufficient. (Mark 7) What governs our mind, fleshly sin or God's Law? (Rom 8:5-7)
What is the “Law”?
Traditionally Reformed theology (except Lutheranism) has divided the Mosaic law into three categories: "ceremonial, judicial and moral" with moral law being the most significant. These categories are broadly useful but their strict application could imply that some laws are no longer relevant to the modern Christian. Doug Moo in The Law and Gospel helpfully suggests God's eternal law sits behind the Mosaic Law. This also makes sense of the emphasis on the moral aspect of the Mosaic Law.
Scripture distinguishes between "God's Law" and the commandments given to Moses. (1 Cor 9:21) The summary of the Law provided by Jesus (Matt 22:40) and echoed by the Apostle Paul (Rom 13:8-10) indicate that there is an eternal essence of the Law that is more than its expression at Mount Sinai (Hosea 6:6 & Gal 6:2). It also seems that God's Law, his eternal decrees, are known to the Gentiles. (Rom 1:32) So it would be safe to say that God's eternal or moral law sits behind, the law written on our hearts (and first expressed to Adam in the Garden of Eden), given to Moses or the commands given in the New Testament.
How were people saved in the Old Testament?
Prior to Jesus, faithful people trusted God and his ultimate promise of a messiah. (Gen 15:6) The Law with it's sacrificial system wasn't designed to justify people. (Acts 13:29 & Gal 3:21) "God desires mercy not sacrifice."(Ps 51:16-17) In Jesus God's promises are fulfilled (2 Cor 1:20) and we trust his work for our justification. (Rom 3:21-27)
What guides our application of the Law today?
- Fulfilled in Christ: Jesus fulfils the Law, (Matt 5:17) He is the "culmination of the Law." (Rom 10:4) He sets aside "the Law with its commands and regulations" (Eph 2:15) and also has "canceled the charge of our legal indebtedness." (Col 2:14)
- Freedom (indwelling of the Holy Spirit): We are no longer under the law (Rom 6:14-15) but "have been released from the law so that we can serve in the new way of the Spirit."(Rom 7:6) Strangely this new era of the law gives us freedom, (James 2:12) because we died to law in order to live for God. (Gal 2:19)
- Different applications: But the earthly Law (in all it's expressions) has not been abolished (Matt 5:18) because "we know that the Law is good if one uses it properly." (1 Tim 1:8) "We've been released from the Law so that we serve in the new way of the Spirit." (Rom 7:6)
Practically what does this all look like?
Pulling all these thread together means that although we no longer have to offer animal sacrifices or wear non-mixed clothing, the principles of God's holiness and our sinfulness remain. The Law has been fulfilled in Christ, we have freedom to take our day of rest on Tuesday, but we're still called to obey God and God's eternal Law sits behind every command in Scripture.