Pope Leo XIII, of pious memory, wrote eleven encyclicals about the Holy Rosary. I've listed them below with links and I wanted to share with you what I thought were some great quotes with some comments.
1. Iucunda Semper Expectatione (On the Rosary)
"It is certain, therefore, that she suffered in the very depths of her soul with His most bitter sufferings and with His torments. Moreover, it was before the eyes of Mary that was to be finished the Divine Sacrifice for which she had borne and brought up the Victim."
2. Laetitiae Sanctae (Commending Devotion to the Rosary)
"There are three influences which appear to Us to have the chief place in effecting this downgrade movement of society. These are -- first, the distaste for a simple and laborious life; secondly, repugnance to suffering of any kind; thirdly, the forgetfulness of the future life...For We are convinced that the Rosary, if devoutly used, is bound to benefit not only the individual but society at large."
What more can restore the dignity of simple tasks (the simplicity of the prayer), suffering (meditating on Christ's life), and the future ("at the hour of our death") than praying the Holy Rosary?
3. Magnae Dei Matris (On the Rosary)
"It pleased Christ to take upon Himself the Son of Man, and to become thereby our Brother, in order that His mercy to us might be shown most openly; for "it behooved him in all things to be made like unto his brethren that he might become a merciful and faithful high priest before God."[Heb 2:17] Likewise because Mary was chosen to be the Mother of Christ, our Lord and our Brother, the unique prerogative was given her above all other mothers to show her mercy to us and to pour it out upon us."
4. Octobri Mense (On the Rosary)
"The Eternal Son of God, about to take upon Him our nature for the saving and ennobling of man, and about to consummate thus a mystical union between Himself and all mankind, did not accomplish His design without adding there the free consent of the elect Mother, who represented in some sort all human kind, according to the illustrious and just opinion of St. Thomas, who says that the Annunciation was effected with the consent of the Virgin standing in the place of humanity...Thus as no man goeth to the Father but by the Son, so no man goeth to Christ but by His Mother...We adore the beloved Savior, lavish of His blood and of His life; we dread the inexorable Judge...[Mary] is the mighty Mother of the Almighty; but-what is still sweeter -- she is gentle, extreme in tenderness, of a limitless loving-kindness. As such God gave her to us."
5. Superiore Anno (On the Recitation of the Rosary)
"May our Heavenly Patroness, invoked by us through the Rosary, graciously be with us and obtain that, all disagreements of opinion being removed and Christianity restored throughout the world, we may obtain from God the wished for peace in the Church."
Even as divisions within the Church plague us, may we implore the one who drew the disciples together with her in the upper room, who constantly seeks to watch over her Son's prayer, "that they all may be one" (John 17:21).
6. Supremi Apostolatus Officio (On Devotion to the Rosary)
"We have deemed it most opportune for similar reasons to institute solemn prayers and to endeavor by adopting those addressed to the Blessed Virgin in the recital of the Rosary to obtain from her son Jesus Christ a similar aid against present dangers. You have before your eyes, Venerable Brethren, the trials to which the Church is daily exposed; Christian piety, public morality, nay, even faith itself, the supreme good and beginning of all the other virtues, all are daily menaced with the greatest perils...That great saint indeed, divinely enlightened, perceived that no remedy would be more adapted to the evils of his time than that men should return to Christ, who "is the way, the truth, and the life," by frequent meditation on the salvation obtained for Us by Him, and should seek the intercession with God of that Virgin, to whom it is given to destroy all heresies. He therefore so composed the Rosary as to recall the mysteries of our salvation in succession, and the subject of meditation is mingled and, as it were, interlaced with the Angelic salutation and with the prayer addressed to God, the Father of Our Lord Jesus Christ."
7. Vi E Ben Noto (On the Rosary and Public Life)
"Let it be your work, venerable brethren, to revive this Christian feeling among your people, an interest in the Catholic cause, a confidence in Our Lady' help, and a spirit of prayer. It is certain that the august Queen, invoked thus well by her man sons, would deign to hear their prayer, console Us in Our sorrow, and crown Our efforts for the Church...by granting better times."
8. Adiutricem (On the Rosary)
"It is mainly to expand the kingdom of Christ that We look to the Rosary for the most effective help. On many occasions We have declared that the object which at the present time engrosses Our most earnest attention, is the reconciliation to the Church of nations which have become separated from her. We recognize, at the same time, that the realization of Our hopes must be sought chiefly in prayer and supplication addressed to almighty God...The mystery of Christ's immense love for us is revealed with dazzling brilliance in the fact that the dying Saviour bequeathed His Mother to His disciple John in the memorable testament: "Behold thy son." Now in John, as the Church has constantly taught, Christ designated the whole human race, and in the first rank are they who are joined with Him by faith. It is in this sense that St. Anselm of Canterbury says: "What dignity, O Virgin, could be more highly prized than to be the Mother of those to whom Christ deigned to be Father and Brother!"
9. Augustissimae Virginis Mariae (On the Confraternity of the Holy Rosary)
"God predestined her from all eternity to be the Mother of the Incarnate Word, and for that reason so highly distinguished her among all His most beautiful works in the triple order of nature, grace and glory, that the Church justly applies to her these words: "I came out of the mouth of the Most High, the first-born before all creatures" (Ecclus 24:5).
10. Diuturni Temporis (On the Rosary)
"Impelled, therefore, by a constant desire that Christians should ever be convinced of the efficacy and dignity of the Rosary of Our Lady, We first of all pointed out that the origin of this form of prayer is divine rather than human, showing it to be an admirable garland woven from the Angelic Salutation, together with the Lord's Prayer, joined to meditation, and that this form of prayer was most powerful and particularly efficacious for attaining eternal life. For besides the special excellence of the prayers, it affords a powerful protection to faith and conspicuous models of virtue in the mysteries proposed for contemplation. We showed also how easy the devotion is and how suited to the people, offering an absolutely perfect model of domestic life in meditation on the Holy Family at Nazareth, and that therefore Christendom had never failed to experience its salutary effects."
11. Fidentem Piumque Animum (On the Rosary)
"The Fathers and Doctors in subsequent times have taught that this is a matter of such grave necessity, that if men neglect it they hope in vain for eternal salvation. Every one who prays finds the door open to impetration, both from the very nature of prayer and from the promises of Christ. And we all know that prayer derives its chief efficacy from two principal circumstances: perseverance, and the union of many for one end. The former is signified in those invitations of Christ so full of goodness: ask, seek, knock (Matt 7:7), just as a kind father desires to indulge the wishes of his children, but who also requires to be continually asked by them and as it were wearied by their prayers, in order to attach their hearts more closely to himself. The second condition Our Lord has born witness to more than once: If two of you shall consent upon earth concerning anything whatsoever they shall ask, it shall be done to them by My Father who is in heaven. For where there are two or three gathered in My name, there am I in the midst of them (Matt 18:19-20)."
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In summary:
PRAY THE ROSARY!