Mary, the Mother of ALMIGHTY GOD is The Immaculate Virgin, The Co-Redeemer, The Mediatrix of Graces, The Most Holy Queen of Heaven and Earth
Excerpts below are from the full article here-
Our Lady is Co-Redeemer and Universal Mediatrix …
The role of Co-Redeemer
a. Leo XIII
"And truly the Immaculate Virgin, pre-chosen to be the Mother of God and for this reason made Co-Redeemer of the human race, has a power and favor before her Son that is greater than any creature – either human or angelic – was or ever will be able to obtain." (Encyclical Supremi apostolatus, § 2, pp. 67-68)
"The Most Holy Virgin is Mother of God, but she is also mother of all Christians whom she has generated on Mount Calvary in the infinite suffering of the Redeemer; similarly Jesus Christ is, in a certain way, the first-born of Christians, who by adoption and the redemption, are His brothers." (Encyclical Quamquam pluries, §3, p. 117)
"When she offered herself to God as His slave, to further become His mother, and when in the Temple she consecrated herself entirely to Him together with her Son, by reason of these two facts, she became a participant in the sorrowful expiation of Christ, to the advantage of the human race." (Encyclical Iucunda semper, § 3, p. 205)
"As we contemplate in the last and more piteous of these Mysteries, there stood by the Cross of Jesus His Mother, who, moved by an intense love for us so that she might have us as her children, generously offered to Divine Justice her own Son, and with Him died in her heart, pierced by the sword of sorrow." (Ibid., p. 207.)
Co-Redeemer & Mediatrix: "From on high, according to the design of God, she watches over the Church, assisting and protecting her as a mother; so that after being the cooperator in the human Redemption, she also became, through the unlimited power conferred upon her, the dispenser of the graces that always flow from the Redemption." (Encyclical Adjutricem populi, § 7, p. 223)
b. St Pius X
Co-Redeemer & Mediatrix: "Further, to the Most Holy Mother of God is due not only the honor of having furnished the material of His flesh to the Only Son of God, who was to be born with human members, so that be prepared the Victim for the salvation of men; but hers also was the role of protecting and nurturing that Victim and, at the appointed time, presenting him for the sacrifice.
"From this came that uninterrupted community of life and sorrows of the Mother and the Son, so that to both of them in an equal way, the words of the Prophet can be applied: 'My soul is consumed in sorrow and my years in groans.' (Ps 30:11)
"And when the supreme hour of the Son came, at the foot of the Cross of Christ there stood His Mother, not merely absorbed in contemplating the cruel spectacle, but rejoicing that her Only Son was offered for the salvation of mankind; and she participated in His Passion so entirely that, if it had been possible, she would gladly have borne herself all the torments that her Son bore.
"From this commonality of will and suffering between Mary and Christ, she merited to become the Reparatrix of the lost mankind, and therefore the Dispensatrix of all the gifts that Our Savior purchased for us with His Death and His Blood.
"It cannot be denied, of course, that the distribution of such gifts is the proper and private right of Jesus Christ, for they were procured for us only from His death and by His power He is the Mediator between God and men. Nevertheless, by this mentioned communality of sorrow and affliction between Mother and Son, it was given to the august Virgin the role of being the most powerful Mediatrix and Advocate of the whole world before her Only Begotten Son." (Encyclical Ad diem illud, §§ 12-13, p. 313)
B. The role of Mediatrix
a. Pius IX
"Thus we repose our most trustful hope in the Most Holy Virgin, who all fair and immaculate has crushed the poisonous head of the most cruel serpent and has brought salvation to the world; in her who is the glory of the Prophets and Apostles, the honor of the Martyrs, the crown and joy of all Saints, the most secure refuge and most faithful helper of all who are in danger; in her who is the most powerful Mediatrix and Conciliatrix of the world before her Only Begotten Son, the most shining glory and ornament of the Church and her most impregnable stronghold. We reaffirm our hope in her who has always destroyed all heresies, has saved the faithful people from the most grave evils of all kinds." (Apostolic Letter Ineffabilis Deus, §31, p. 55)
"And since she has been appointed by God to be the Queen of Heaven and Earth and is exalted above all the choirs of Angels and all the ranks of Saints, she sits at the right hand of her Only Begotten Son, Our Lord Jesus Christ, and with her most powerful maternal prayers she pleads. What she asks, she obtains. Her pleas can never be unheard." (Ibid., §32, p. 7)
b. Leo XIII
"She [the great Mother of God, the Virgin Mary], in truth the Mediator before God of our peace and Dispenser of the celestial graces, is seated in Heaven on the highest throne of power and glory so that she may bestow her patronage on men, who, through so many labors and fights are striving to reach that celestial homeland." (Encyclical Supremi apostolatus, §1, p. 67)
Christ established Our Lady as Queen of Heaven & Earth and made her universal Mediatrix of all graces
"Consequently, we can with all truth and rigor affirm that, by the will of God, nothing can be communicated from the immense treasure of graces gathered by Christ – for we know that 'the glory and the truth came from Jesus Christ' – if it is not through Mary. Thus, as no man can approach the Eternal Father except through the Son, so also no man can approach Christ except through His Mother." (Encyclical Octobre mense, §4, pp.135-137)
"Our supplicating recourse to the patronage of Mary is based upon her role as Mediatrix of divine grace: the office that she – most pleasing to God for her dignity and merits and surpassing in power all the Angels and Saints – continuously exercises for us before the throne of the Most High." (Encyclical Iucunda semper, §2, p. 205)
"Then, after invoking the Father with the noblest of the prayers, our supplicating voice turns from the throne of His Majesty to Mary. Thus is confirmed that mentioned law of her merciful mediation and intersession, expressed by St. Bernardine of Siena with these words: 'Every grace dispensed on this earth passes through three successive orders. From God it is communicated to Christ, from Christ to the Virgin and from the Virgin to us.'" (Ibid., § 5, p. 207)
c. Pius XI
"He [God] who made the peoples and nations for health (Wisdom 1:14) without a doubt will not let perish those whom He has redeemed with His Precious Blood, nor will He ever abandon His Church. But, rather … we must beseech God through the mediation of the Blessed Virgin, so dear to Him, since, to use the words of St. Bernard, 'Such is the will of God, who has wished that we should have all things through Mary.'" (Encyclical Ingravescentibus malis, § 8, p. 417)
d. Pius XII
"Therefore, as Bernard affirms ' Such is the will of God, who has wished that we should have all things through Mary,' all must have recourse to Mary: They should rest on her altar their petitions, their tears, their sorrows and ask her solace and comfort. … The Blessed Virgin is indeed so powerful before God and her only Begotten Son that, as [Dante] Alighieri sings: 'He who seeks grace without recourse to you [Our Lady], would have his wish fly upward without wings.'" (Letter Superiore Anno, April 15, 1940, §3, p. 439)
"We have another reason for confidence and hope. Before the throne of the Most High we have the Most Benign Mother of God and our Mother, who, by her powerful intercession can securely ask from Him everything for us." (Letter Quamvis plane, April 20, 1941, §3, p. 445)
"Blessed be the Lord God and Father of Our Lord Jesus Christ, the Father of mercy and the God of all consolations, who console us in all our tribulations. And with the Lord may she also be blessed whom He has appointed Mother of mercy, Queen and our most beloved Advocate, Mediatrix of His graces, Dispenser of His treasures! (Radio-message Bendito seja o Senhor, May 13, 1946, §1, p. 514)
"May she, who has given us Jesus … she who is our most benign Mother and who in face of every danger has always shown herself to be our powerful helper and mediatrix of graces, may she obtain for us that, even amidst the most grievous anguishes that we face, a just solution for contentions and that a firm and free peace may finally dawn resplendent for the Church and for all nations." (Encyclical Auspicia quaedam, §10, p. 573)