Matthew and Luke have two versions of Jesus' great sermon. Matthew's is the most famous version, called the Sermon on the Mount, (found in chapters 5-7) and Luke's is called the Sermon on the Plain (in chapter 6, beginning at verse 19). Although they have slightly different content, they have the same outline and are basically the sermon that Jesus taught all throughout his ministry. Matthew added much more, and gave a different sense to the sermon. He gives the sense that Jesus is a new Moses, standing at the mountain, giving a new law.
There is no question as to this is exactly what Jesus was doing, giving a new law. But in a sense, Jesus was giving a commentary on every law book that ever existed. Matthew's version gives us a specific look at Moses' law, with Jesus contrasting his interpretation of Moses with other teachers of Moses. But every law book is commented on by Jesus' sermon, every church manual, every policy book for every government or corporation.
There are a few basic themes in the sermon:
First, that God is on the side of the outcast and poor, not the powerful. Jesus emphasizes in both sermons that it is the poor, the hungry, the persecuted, the meek that are granted God's blessings, not the wildly religious or those well-off. Thus, if we are to gain God's favor, we are better off to be lowly than to be great and religious.
Second, Jesus emphasizes that all laws are to be marginalized by love. Mercy, love, compassion, forgiveness are going to survive to the next age, while judgment and vengeance will not. If we want to survive, we must focus on love, not on our limited notions of "justice".
Finally, Jesus emphasizes obedience. Not obedience to the specific laws of men, but obedience to the higher law that He is teaching. If we do not follow the higher law, then being a good citizen, a good mother, a good employee on earth will mean nothing in the long run.
In the end, the whole of what Jesus said can be summarized like this:
If you want to be on the in track with God, be a rebel for love. Be punished for loving too much. Get rejected because you had compassion. In the end, you will benefit, because God is a God of justice for the unfairly harmed.