The Sermon on the Mount

When Israel came into the promised land they were to set themselves upon the two mountains, Ebal and Gerizim, which stood over Shechem where the tabernacle was to dwell, and the congregation would stand half on one side, half on the other, and they would shout the words of the Lord at each other. 

Deut 11:29 "And it shall come to pass, when the LORD your God has brought you in unto the land where you go to possess it, that you shall put the blessing upon mount Gerizim, and the curse upon mount Ebal."-

Joshua 8:33 has the record of them carrying this out:

And all Israel, sojourner as well as native born, with their elders and officers and their judges, stood on opposite sides of the ark before the Levitical priests who carried the ark of the covenant of the LORD, half of them in front of Mount Gerizim and half of them in front of Mount Ebal, just as Moses the servant of the LORD had commanded at the first, to bless the people of Israel. 

 In Deut chapter 27 this is more fully explained, they were to put an alter on the cursing mountain, and ask God for peace.

4-7a "Therefore it shall be when all of you be gone over Jordan, that all of you shall set up these stones, which I command you this day, in mount Ebal, and you shall smear them with plaster. And there shall you build an altar unto the LORD your God, an altar of stones: you shall not lift up any iron tool upon them. You shall build the altar of the LORD your God of whole stones: and you shall offer burnt offerings thereon unto the LORD your God: And you shall offer peace offerings."

 Verses 15-26 has the record of what they shouted from Ebal

Cursed be the man that makes any graven or molten image, an abomination unto the LORD, the work of the hands of the craftsman, and puts it in a secret place. And all the people shall answer and say, Amen. 16 Cursed be he that sets light by his father or his mother. And all the people shall say, Amen.
Cursed be he that removes his neighbour's landmark. And all the people shall say, Amen.
Cursed be he that makes the blind to wander out of the way. And all the people shall say, Amen.
Cursed be he that perverts the judgment of the stranger, fatherless, and widow. And all the people shall say, Amen.
Cursed be he that lies with his father's wife; because he uncovers his father's skirt. And all the people shall say, Amen.
Cursed be he that lies with any manner of beast. And all the people shall say, Amen.
Cursed be he that lies with his sister, the daughter of his father, or the daughter of his mother. And all the people shall say, Amen.
Cursed be he that lies with his mother in law. And all the people shall say, Amen.
Cursed be he that strikes his neighbour secretly. And all the people shall say, Amen.
Cursed be he that takes reward to slay an innocent person. And all the people shall say, Amen.
Cursed be he that confirms not all the words of this law to do them. And all the people shall say, Amen.  

Then the chapter ends. Where is the record of what they shouted from Gerizim? Where is the other half of the account? Why is the scale loaded with bricks on one side and nothing on the other? The account is so off balanced because blessing they shouted is conspicuously, hugely, glaringly absent from the record.
Ultimately we know that they as a people were never entitled to any blessing, and so were to remember their failure, and so they were only entitled to the curses.
No Gerizim. No blessedness.

Having this in mind is the only way to understand this:

And seeing the multitudes, He went up on a mountain, and when He was set, His disciples came to Him:
And He opened His mouth, and taught them, saying,
Blessed are the poor in spirit: for theirs is the kingdom of heaven.
Blessed are they that mourn: for they shall be comforted.
Blessed are the meek: for they shall inherit the earth.
Blessed are they which do hunger and thirst after righteousness: for they shall be filled.
Blessed are the merciful: for they shall obtain mercy.
Blessed are the pure in heart: for they shall see God.
Blessed are the peacemakers: for they shall be called the children of God.
Blessed are they which are persecuted for righteousness' sake: for theirs is the kingdom of heaven.
Blessed are all of you, when men shall revile you, and persecute you, and shall say all manner of evil against you falsely, for my sake.

Here is the One who balances the cursing that comes from the law, the blessings that were shouted from the mountain. They were held back, kept mysterious, waiting until they would be found in Christ. And here is the one who does not need an alter to ask for forgiveness and peace, He is their peace, He is giving them forgiveness. It's the difference between asking and giving. It marks an entirely new epoch in the Bible's narrative.
This text, it's more than just a guidebook on how to be happy, it's the end of the law, the end of the cursings, the fulfillment of the promise. As John said, the law came through Moses, but grace and truth came through Christ.