Matthew 5:17-20

Fulfillment of the Law and Prophets.
v.17 Jesus came to fulfill the law of Moses and the rest of the OT. Jesus' teaching does not contradict the OT law, but rather unfolds it and transcends it. Christ is the end or goal of the law (Rom 10:4). The law and the prophets point to him. Jesus did not oppose the law, but rather the illegitimate interpretation of it that stressed regulations instead of internal character.
v.18 The law is permanent (not a letter or stroke of the pen will pass away) until all has been accomplished (heaven and earth pass away). Correct interpretation of the OT law must take into account the NT teachings. Jesus gives examples of such NT interpretations of OT law in the coming verses (v.21-48).
v.19 Jesus' teaching and the OT, properly interpreted, must be obeyed (perfection, v.48). The verse seems to indicate graduations of honor/dishonor within God's kingdom. Teachers must not only follow the commands, but teach others to do the same.
v.20 The righteousness that the law pointed to is required for admission to the kingdom. (This of course is only possible for us through Christ.) The Pharisees had outward conformity to many regulations but still had impure hearts inside.

Read Matthew 5:17-20