Here are some papal thoughts on the supreme mystery of our Catholic faith.

The Holy Trinity

From St. Pope John Paul II

 “Glory to the Father, the Son and the Holy Spirit: to God who is, who was, and who is to come” (Gospel acclamation).

The Church ceaselessly repeats this praise to the Most Holy Trinity. Indeed, Christian prayer begins with the sign of the Cross: “In the name of the Father and of the Son and of the Holy Spirit”, and often ends with the Trinitarian doxology: “Through our Lord Jesus Christ, your Son, who lives and reigns with you and the Holy Spirit, one God, for ever and ever”.

Every day constant praise of the Trinity rises to God from the community of believers; today, however, the first Sunday after Pentecost, we are celebrating this great mystery of faith in a special way.

Gloria Tibi, Trinitas, aequalis, una Deitas, et ante omnia saecula et nunc, et in perpetuum! — “All glory belongs to you, Holy Trinity, one God, before all ages, now and for ever!” (First Vespers of the Solemnity of the Blessed Trinity).

In this liturgical formula we contemplate the mystery of the ineffable unity and inscrutable Trinity of God: Father, Son and Holy Spirit. This is what we profess in the Apostles’ Creed:

“I believe in God …
I believe in Jesus Christ, his only Son, our Lord …
He was conceived by the Holy Spirit, born of the Virgin Mary”.

And again, in the Nicene-Constantinopolitan Creed:
“We believe in the Holy Spirit, the Lord, the giver of life, who proceeds from the Father and the Son. With the Father and the Son he is worshiped and glorified. He has spoken through the prophets”.

This is our faith! This is the Church’s faith! This is the God of our faith: Father, Son and Holy Spirit!

25 May 1997, Visit to the Roman Parish of Saint Linus | John Paul II (vatican.va)

From Pope Benedict XVI

After the Easter Season which culminated in the Feast of Pentecost, the liturgy provides for these three Solemnities of the Lord:

today, Trinity Sunday;

next Thursday, Corpus Christi which in many countries, including Italy, will be celebrated next Sunday;

and finally, on the following Friday, the Feast of the Sacred Heart of Jesus.

Each one of these liturgical events highlights a perspective by which the whole mystery of the Christian faith is embraced: and that is, respectively the reality of the Triune God, the Sacrament of the Eucharist and the divine and human centre of the Person of Christ. These are truly aspects of the one mystery of salvation which, in a certain sense, sum up the whole itinerary of the revelation of Jesus, from his Incarnation to his death and Resurrection and, finally, to his Ascension and the gift of the Holy Spirit.

The Virgin Mary, in her docile humility, became the handmaid of divine Love: she accepted the Father’s will and conceived the Son by the power of the Holy Spirit. In her the Almighty built a temple worthy of him and made her the model and image of the Church, mystery and house of communion for all human beings. May Mary, mirror of the Blessed Trinity, help us to grow in faith in the Trinitarian mystery. Angelus, 7 June 2009, Solemnity of the Most Holy Trinity | BENEDICT XVI (vatican.va)

From Pope Francis

On this feast day in which we celebrate God: the mystery of the one God. And this God is the Father and the Son and the Holy Spirit. Three persons, but God is one! The Father is God; the Son is God; the Spirit is God. But they are not three gods: it is one God in three Persons. It is a mystery that Jesus Christ revealed to us: the Holy Trinity. Today we pause to celebrate this mystery, because the Persons are not adjectives of God, no. They are real, diverse, different Persons; they are not — as that philosopher used to say — ‘emanations of God’, no, no! They are Persons.

There is the Father to whom I pray with the Our Father; there is the Son, who gave me redemption, justification; there is the Holy Spirit who abides in us and inhabits the Church. And this speaks to our heart because we find it encompassed in that expression of Saint John which summarizes all of Revelation: “God is love” (1 Jn 4:8-16). The Father is love; the Son is love; the Holy Spirit is love. And inasmuch as he is love, God, while being one alone, is not solitude but communion, among the Father, the Son and the Holy Spirit.

Because love is essentially a gift of self, and in its original and infinite reality it is the Father who gives himself by generating his Son, who in turn gives himself to the Father, and their mutual love is the Holy Spirit, the bond of their unity. It is not easy to understand, but we can live this mystery, all of us, we can live it a great deal. Angelus, 30 May 2021, Trinity Sunday | Francis (vatican.va)

And to reflect further on the Trinity
here is a non-papal homily from Bishop Robert Barron
in which he quotes B16.