CATECHISM OF THE CATHOLIC CHURCH
SECOND EDITION

Paragraphs 254–257

254 The divine persons are really distinct from one another. "God is one but not solitary." "Father", "Son", "Holy Spirit" are not simply names designating modalities of the divine being, for they are really distinct from one another: "He is not the Father who is the Son, nor is the Son he who is the Father, nor is the Holy Spirit he who is the Father or the Son." They are distinct from one another in their relations of origin: "It is the Father who generates, the Son who is begotten, and the Holy Spirit who proceeds." The divine Unity is Triune.
255 The divine persons are relative to one another. Because it does not divide the divine unity, the real distinction of the persons from one another resides solely in the relationships which relate them to one another: "In the relational names of the persons the Father is related to the Son, the Son to the Father, and the Holy Spirit to both. While they are called three persons in view of their relations, we believe in one nature or substance." Indeed "everything (in them) is one where there is no opposition of relationship." "Because of that unity the Father is wholly in the Son and wholly in the Holy Spirit; the Son is wholly in the Father and wholly in the Holy Spirit; the Holy Spirit is wholly in the Father and wholly in the Son."
256 St. Gregory of Nazianzus, also called "the Theologian", entrusts this summary of Trinitarian faith to the catechumens of Constantinople:
Above all guard for me this great deposit of faith for which I live and fight, which I want to take with me as a companion, and which makes me bear all evils and despise all pleasures: I mean the profession of faith in the Father and the Son and the Holy Spirit. I entrust it to you today. By it I am soon going to plunge you into water and raise you up from it. I give it to you as the companion and patron of your whole life. I give you but one divinity and power, existing one in three, and containing the three in a distinct way. Divinity without disparity of substance or nature, without superior degree that raises up or inferior degree that casts down. . . the infinite co-naturality of three infinites. Each person considered in himself is entirely God. . . the three considered together. . . I have not even begun to think of unity when the Trinity bathes me in its splendor. I have not even begun to think of the Trinity when unity grasps me. . .
257 "O blessed light, O Trinity and first Unity!" God is eternal blessedness, undying life, unfading light. God is love: Father, Son and Holy Spirit. God freely wills to communicate the glory of his blessed life. Such is the "plan of his loving kindness", conceived by the Father before the foundation of the world, in his beloved Son: "He destined us in love to be his sons" and "to be conformed to the image of his Son", through "the spirit of sonship". This plan is a "grace [which] was given to us in Christ Jesus before the ages began", stemming immediately from Trinitarian love. It unfolds in the work of creation, the whole history of salvation after the fall, and the missions of the Son and the Spirit, which are continued in the mission of the Church.