Did Jesus Abolish "thou shalt not murder, or thou shalt not commit adultery?"

Yes and No.

Jesus did not completely abolish the Mosaic law. However, the requirements of the law still remain. Instead, Jesus made a way to fulfill the laws requirements instead. He abolished the penalty of the Law for those who have faith in Christ. Remember, the purpose of the law was to show you how sinful you are. Since we have come to Christ and have faith in what He did on the cross, God no longer counts the law against us because of Christ. God’s grace has freed us from the penalty of the law. There is no longer a Mosaic law for us to follow if establish it ourselves. It’s by our faith in Christ that we have been counted righteous.

Concerning the answer, “No,” Paul said, “Well then, if we emphasize faith, does this mean that we can forget about the law?” In fact, without having faith in Christ, we are still guilty of the law and will have to pay the penalty, which is death.

Paul explains why we are no longer subject to the law.

Romans 3:21-31 "But now God has shown us a way to be made right with him without keeping the requirements of the law, as was promised in the writings of Moses and the prophets long ago. We are made right with God by placing our faith in Jesus Christ. And this is true for everyone who believes, no matter who we are. For everyone has sinned; we all fall short of God’s glorious standard. Yet God, with undeserved kindness, declares that we are righteous. He did this through Christ Jesus when he freed us from the penalty for our sins. For God presented Jesus as the sacrifice for sin. People are made right with God when they believe that Jesus sacrificed his life, shedding his blood. This sacrifice shows that God was being fair when he held back and did not punish those who sinned in times past; for he was looking ahead and including them in what he would do in this present time. God did this to demonstrate his righteousness, for he himself is fair and just, and he declares sinners to be right in his sight when they believe in Jesus. Can we boast, then, that we have done anything to be accepted by God? No, because our acquittal is not based on obeying the law. It is based on faith. So we are made right with God through faith and not by obeying the law. After all, is God the God of the Jews only? Isn’t he also the God of the Gentiles? Of course he is. There is only one God, and he makes people right with himself only by faith, whether they are Jews or Gentiles. Well then, if we emphasize faith, does this mean that we can forget about the law? Of course not! In fact, only when we have faith do we truly fulfill the law."

To reiterate what Paul explained, because we have placed our faith in Christ, we now establish or fulfill (complete, establish, finish, end, satisfy) the law.

This law is simple. It is to love the Lord God with all your heart, soul, mind and strength and to love your neighbor as you love yourself.
*Romans 13:8 “If you love your neighbor, you will fulfill the requirements of God’s law.”
*Romans 13:10 “Love does no wrong to others, so love fulfills the requirements of God’s law.”
*Galatians 5:14 “For the whole law can be summed up in this one command: “Love your neighbor as yourself.”

The bottom line is that when we are led by the Spirit of God, and allow our faith in Christ to fill our lives, the natural response is to love God and love others. When we love others, we will not commit adultery and we will not murder people. When we love God and others, we will not steal from our friends and we will not treat others unfairly. Therefore, we establish the law and become a law unto ourselves because of our faith in Christ and our love for others.