Text in red are my additions.
By way of introduction here is what the Glossary of the Catechism of the Catholic Church has to say concerning the Beatitudes: BEATITUDES: The teachings of Jesus in the Sermon on the Mount on the meaning and way to true happiness (cf. Mt 5:1–12; Lk 6:20–23). These teachings reflect the promises made to the chosen people since Abraham; they portray the countenance of Christ and describe his charity. Moreover, by shedding light on the actions and attitudes characteristic of the Christian life, they describe the vocation of all the faithful (1716) [Catholic Church. Catechism of the Catholic Church. 2nd Ed. Washington, DC: United States Catholic Conference, 2000.] For more on the beatitudes one can profitably consult the CCC 1716-1729.
Mt 5:1. And seeing the multitudes, he went up into a mountain, and when he was set down, his disciples came unto him.
It is a question whether St. Matthew here and St. Luke 6:20-49 are giving the same identical discourse. It is possible that our Lord may have repeated the same discourse more than once, but it is probable that St. Matthew is only giving with more detail and greater development that of which St. Luke has preserved for us only an abridgment. The differences may all be explained by
saying that one omits what he knows the other has. Our Lord spent the night in prayer and on the morrow chose His twelve Apostles. To them and to the multitude that had gathered a little further down the hill. He immediately delivered the Sermon on the Mount. Cf. Mt 6:12-17.
A mountain, which was probably that called the Horns of Hattin, about two hours’ distance from Tiberias (This is most likely a reference to the city of Tiberias, located on the west side of the Galilee, or to the Galilee itself, which was sometimes called Tiberias see Jn 21:1).
Mt 5:2. And opening his mouth, he taught them, saying:
And opening his mouth. Hitherto our Lord had spoken by the mouth of His prophets and by the silent voice of His own miracles; but now He has determined to give personal utterance to His teachings. The Sermon on the Mount is an exposition of our Lord’s ideas of happiness, wisdom and justice. Its aim throughout is to show the contrast between the principles of His kingdom and the principles which prevail in the world and in an imperfect Judaism, It may be divided in three parts: (a) Jesus promises happiness to those whom He calls; (b) He prescribes justice to those who come; (c) and He recommends wisdom to those who remain with Him (Le Camus).
Mt 5:3. Blessed are the poor in spirit: for theirs is the kingdom of heaven.
Blessed; i.e., happy.
Poor in spirit; i.e., those who are not attached to riches or to the goods of this world, either by desire or by actual possession. It is, in particular, detachment from earthly goods that makes one blessed. See Ps 69:32-33; Is 61:1, Mt 23:12; k 18:9-14. See also CCC 2544-2549.
Mt 5:4. Blessed are the meek : for they shall possess the land.
Meek; i.e., those who for Christ’s sake willingly and patiently endure the evils and hardships of life. By ” the meek ” we are not to understand lifeless and colorless characters; but those who, possessed of real character and vigor, meekly control themselves for the sake of Christ, and out of imitation of Him. See Ps 37:11; Zeph 3:11-12; Mt 11:29.
Shall possess the land. This is commonly understood, after St. Jerome, to refer to the new heaven and the new earth, which the meek shall possess.
Mt 5:5. Blessed are they that mourn : for they shall be comforted.
Mourn; i.e., those who grieve for their own and for others’ offenses, out of love of God. are blessed, happy. See Ps 51:17; Isa 57:18-21; 61:1-3; Jer 31:13; Rev 7:17; 21:4.
Mt 5:6. Blessed are they that hunger and thirst after justice : for they shall have their fill.
Hunger and thirst, etc. ; i.e., happy are those who are subjected to real hunger and thirst, because justice is not done them, but who nevertheless patiently bear the wrong done them for God’s sake. See Isa 55:1-2; Mt 6:33; 2 Tim 2:22; 1 Pet 3:12.
Mt 5:7. Blessed are the merciful: for they shall obtain mercy.
Merciful; i.e., happy are those who try to alleviate the miseries of others, who charitably overlook and forgive the sins and mistakes of others; as they really forgive others, so shall they be forgiven. See Ex 34:6-7; Dan 9:9; Mt 6:12, 14-15; 18:21-35; Lk 6:36; Jam 2:13.
Mt 5:8. Blessed are the clean of heart: for they shall see God.
Clean of heart; i.e., happy are those who observe not only purity and chastity of body, but general purity and simplicity of conscience. It is certain that chastity of life will not only have an unspeakable reward hereafter, but that it leads to clearness of vision here below, in things purely natural, and especially in things supernatural. See Ps 24:3-5; 51:10; 73:1; 1 Jn 3:2-3.
Mt 5:9. Blessed are the peacemakers: for they shall be called the children of
Peacemakers; i.e., those who strive to reconcile the differences between others. See Ps 34:14; Matt 5:44-45; Rom 12:18; 14:19; 2 Tim 2:22; Jam 3:1-18.
Mt 5:10. Blessed are they that suffer persecution for justice’ sake: for theirs is the kingdom of heaven.
For justice’ sake; i.e., happy are those who are persecuted on account of their faithfulness to the law of God and to their own duty. It is to be noted that throughout the beatitudes our Lord is continually raising our minds to the things of Heaven; we are not to expect temporal rewards for doing what He has enjoined; we are to look for our recompense hereafter. For this and the remaining two verses see See Jn 15:18-21; 2 Tim 3:10-12; Jam 1:12; 1 Pet 3:14, 17; 4:12-16.
Mt 5:11. Blessed are ye when they shall revile you, and persecute you, and speak all that is evil against you, untruly, for my sake:
Untruly. Our Lord promises no blessedness, no beatitude to those who deserve persecution and reviling; it is only to those who are unjustly so treated.
Mt 5:12. Be glad and rejoice, for your reward is very great in heaven. For so they persecuted the prophets that were before you.
Be glad. Those who suffer for the sake of Christ have every reason to rejoice because of the reward awaiting them hereafter.