What the Catechism of the Catholic Church says on "The Trinity:"

232. "Christians are baptized 'in the name of the Father and of the Son and of the Holy Spirit' [Mt 28:19.] Before receiving the sacrament, they respond to a three-part question when asked to confess the Father, the Son and the Spirit: 'I do.' 'The faith of all Christians rests on the Trinity.' [St. Caesarius of Arles, Sermo 9, Exp. symb.: CCL 103, 47.]"

233. "Christians are baptized in the name of the Father and of the Son and of the Holy Spirit: not in their names, [Cf. Profession of faith of Pope Vigilius I (552): DS 415.] for there is only one God, the almighty Father, his only Son and the Holy Spirit: the Most Holy Trinity."

234. "The mystery of the Most Holy Trinity is the central mystery of Christian faith and life. It is the mystery of God in himself. It is therefore the source of all the other mysteries of faith, the light that enlightens them. It is the most fundamental and essential teaching in the 'hierarchy of the truths of faith'. [GCD 43.] The whole history of salvation is identical with the history of the way and the means by which the one true God, Father, Son and Holy Spirit, reveals himself to men 'and reconciles and unites with himself those who turn away from sin'. [GCD 47.]"

235. "This paragraph expounds briefly (I) how the mystery of the Blessed Trinity was revealed, (II) how the Church has articulated the doctrine of the faith regarding this mystery, and (III) how, by the divine missions of the Son and the Holy Spirit, God the Father fulfils the 'plan of his loving goodness' of creation, redemption and sanctification."

236. "The Fathers of the Church distinguish between theology (theologia) and economy (oikonomia). 'Theology' refers to the mystery of God's inmost life within the Blessed Trinity and 'economy' to all the works by which God reveals himself and communicates his life. Through the oikonomia the theologia is revealed to us; but conversely, the theologia illuminates the whole oikonomia. God's works reveal who he is in himself; the mystery of his inmost being enlightens our understanding of all his works. So it is, analogously, among human persons. A person discloses himself in his actions, and the better we know a person, the better we understand his actions."

237. "The Trinity is a mystery of faith in the strict sense, one of the 'mysteries that are hidden in God, which can never be known unless they are revealed by God'. [Dei Filius 4: DS 3015.] To be sure, God has left traces of his Trinitarian being in his work of creation and in his Revelation throughout the Old Testament. But his inmost Being as Holy Trinity is a mystery that is inaccessible to reason alone or even to Israel's faith before the Incarnation of God's Son and the sending of the Holy Spirit."

238. "Many religions invoke God as 'Father'. The deity is often considered the 'father of gods and of men'. In Israel, God is called 'Father' inasmuch as he is Creator of the world. [Cf. Dt 32:6; Mal 2:10.] Even more, God is Father because of the covenant and the gift of the law to Israel, 'his first-born son'. [Ex 4:22.] God is also called the Father of the king of Israel. Most especially he is 'the Father of the poor', of the orphaned and the widowed, who are under his loving protection. [Cf. 2 Sam 7:14; Ps 68:6.]"

239. "By calling God 'Father', the language of faith indicates two main things: that God is the first origin of everything and transcendent authority; and that he is at the same time goodness and loving care for all his children. God's parental tenderness can also be expressed by the image of motherhood, [Cf. Is 66:13; Ps 131:2.] which emphasizes God's immanence, the intimacy between Creator and creature. The language of faith thus draws on the human experience of parents, who are in a way the first representatives of God for man. But this experience also tells us that human parents are fallible and can disfigure the face of fatherhood and motherhood. We ought therefore to recall that God transcends the human distinction between the sexes. He is neither man nor woman: he is God. He also transcends human fatherhood and motherhood, although he is their origin and standard: [Cf. Ps 27:10; Eph 3:14; Is 49:15.] no one is father as God is Father."

240. "Jesus revealed that God is Father in an unheard-of sense: he is Father not only in being Creator; he is eternally Father by his relationship to his only Son who, reciprocally, is Son only in relation to his Father: 'No one knows the Son except the Father, and no one knows the Father except the Son and any one to whom the Son chooses to reveal him.' [Mt 11-27.]"

241. "For this reason the apostles confess Jesus to be the Word: 'In the beginning was the Word, and the Word was with God, and the Word was God'; as 'the image of the invisible God'; as the 'radiance of the glory of God and the very stamp of his nature'. [Jn 1:1; Col 1:15; Heb 1:3.]"

242. "Following this apostolic tradition, the Church confessed at the first ecumenical council at Nicaea (325) that the Son is 'consubstantial' with the Father, that is, one only God with him. [The English phrases 'of one being' and 'one in being' translate the Greek word homoousios, which was rendered in Latin by consubstantialis.] The second ecumenical council, held at Constantinople in 381, kept this expression in its formulation of the Nicene Creed and confessed 'the only- begotten Son of God, eternally begotten of the Father, light from light, true God from true God, begotten not made, consubstantial with the Father'. [Niceno-Constantinopolitan Creed; cf. DS 150.]"

243. "Before his Passover, Jesus announced the sending of 'another Paraclete' (Advocate), the Holy Spirit. At work since creation, having previously 'spoken through the prophets', the Spirit will now be with and in the disciples, to teach them and guide them 'into all the truth'. [Cf. Gen 1:2; Nicene Creed (DS 150); Jn 14:17, 26; Jn 16:13.] The Holy Spirit is thus revealed as another divine person with Jesus and the Father."

244. "The eternal origin of the Holy Spirit is revealed in his mission in time. The Spirit is sent to the apostles and to the Church both by the Father in the name of the Son, and by the Son in person, once he had returned to the Father. [Cf. Jn 14:26; Jn 15:26; Jn 16:14.] The sending of the person of the Spirit after Jesus' glorification [Cf. Jn 7:39.] reveals in its fullness the mystery of the Holy Trinity."

245. "The apostolic faith concerning the Spirit was confessed by the second ecumenical council at Constantinople (381): 'We believe in the Holy Spirit, the Lord and giver of life, who proceeds from the Father.' [Nicene Creed; cf. DS 150.] By this confession, the Church recognizes the Father as 'the source and origin of the whole divinity'. [Council of Toledo VI (638): DS 490.] But the eternal origin of the Spirit is not unconnected with the Son's origin: 'The Holy Spirit, the third person of the Trinity, is God, one and equal with the Father and the Son, of the same substance and also of the same nature. . . Yet he is not called the Spirit of the Father alone,. . . but the Spirit of both the Father and the Son.' [Council of Toledo XI (675): DS 527.] The Creed of the Church from the Council of Constantinople confesses: 'With the Father and the Son, he is worshipped and glorified.' [Nicene Creed; cf. DS 150.]"

246. "The Latin tradition of the Creed confesses that the Spirit 'proceeds from the Father and the Son (filioque)'. The Council of Florence in 1438 explains: 'The Holy Spirit is eternally from Father and Son; He has his nature and subsistence at once (simul) from the Father and the Son. He proceeds eternally from both as from one principle and through one spiration... And, since the Father has through generation given to the only-begotten Son everything that belongs to the Father, except being Father, the Son has also eternally from the Father, from whom he is eternally born, that the Holy Spirit proceeds from the Son.' [Council of Florence (1439): DS 1300-1301.]"