When He finished His sermon, the people were astonished, as He had taught them, not as the "letter of the law" scribes and Pharisees did, but "as one having authority" (Matthew 7:28-29). Jesus could preach with conviction and boldness because He saw past the rigid letter of God's commandments to their very spiritual heart and purpose. He could confidently give the law its true meaning and relevance to life.
In essence, Matthew 5 - 7 contain instructions from Jesus for them, and for us today, to go further than the strictly physical application of the law - to God's true intent in it, or as we say, from the letter to the spirit of the law. In His teaching, Jesus states a physical law, often quoting directly from the Old Testament. This base standard is to be met by all those who have made a covenant with God.
Then, He proceeds to amplify the particular law's meaning, usually beginning His amplification with words similar to, "I say to you. . . ." Such words should be a flag to us that Jesus is expanding the scope of the law to include, not just physical actions, but the condition, attitudes, and inclinations of a person's heart. In essence, He is teaching the standards required of His people to attain the Kingdom of God.