Jesus makes it very clear that He did not come to "abolish the Law and the Prophets". Given the clarity of this statement it is amazing the number of people who seem to think He did just that!
The Law refers to the first five books of the Old Testament. The Prophets refers not just to what we think of as the prophets (Isaiah, Jeremiah, Micah etc), but also to what the Jews called the "former prophets", meaning Joshua, Samuel, Kings. And the term "Law and Prophets" meant the whole of the Old Testament.
The Law expressed the heart of God. In sending His Son God's character had not changed, he had not changed His mind. Rather Jesus came to fulfil the Law and the Prophets. He did this by perfectly obeying His Father, and by fulfilling the prophecies of the future salvation.
As I have just said, the Law expresses the heart of God. It was wrong to murder before the ten commandments were given, it was wrong to murder after the commandments were given, and it is still wrong to murder.
Jesus' words here on not one least stroke of the pen disappearing should help us to interpret the Sermon on the Mount. It is said by some that He was overturning what Moses said. This is not true, rather He is getting to the heart of the matter. As we go on through this sermon we will see that many of the supposed "innovations" are actually there in the Law.
It was the Pharisees who were actually guilty of setting aside the requirements of the Law, though they were seeking to the very opposite. Again, we shall see examples of this later in Matthew. We need to take this as a general warning as well, those who seek to defend something most ardently can end up being guilty of destroying it.
The righteousness of Jesus' disciples has to exceed that of all others. Jesus also makes it clear that the righteousness of the Pharisees would not get them into the kingdom of heaven. Note that "kingdom of Heaven" here means "rule of God". Legalism does not get us into the kingdom of Heaven. We can be guilty of applying this in various areas, eg evangelism and tithing. We rightly seek to be a Church who witness to Christ and who give generously, but if we try to achieve these goals by legalism we will end up failing.
Sometimes we can be guilty of teaching tithing as a legalistic thing, we do this from the best of motives, but it will produce the wrong results. But note this too. If we live the Sermon on the Mount then we will be doing much more than a legalistic interpretation of the Law would produce. Likewise, if we have God's generous heart, then we will give much more than any teaching on tithing requires.