Paul's New Testament letter to the Galatians is a good place to begin your study of what the Bible says about God's Law as it was given to Israel through Moses.  Another good place is the New testament book of Romans, especially chapters 4 through 8.

Whenever we read the Bible, we need to keep in mind the who, the what and the where (in time as well as where in location).  Just as any good parent will often give different instructions to a teen than they give to a toddler, so also the God of heaven and earth will have different things to say at different times.  The heart of the message never changes, but the specific instruction and application will often be different.

We are not wiser or more holy in the present age than the people of ancient Israel were.  But we do live at a different point in history.  God still expects us to live holy lives.  But instead of a Law written in stone, believers today have the Law of the Holy Spirit written in our hearts.  This is exactly what the Lord promised through the Old Testament prophet, Jeremiah.

Is the Law of Moses, including the Ten Commandments, still applicable today?  Yes.  But we know that keeping the Law does not give us entrance into heaven.  Eternal life is a gift of God's grace, through faith in Jesus Christ.  The Law exists today to give us an external witness to the will of God revealed to us by the Holy Spirit which indwells every true follower of Jesus Christ.

Along these lines, you may wish to pay special attention to what the Apostle Paul wrote in Galatians, chapter 5.  There he talks about walking in the Spirit in order to be truly free of the Law and its requirements.