The Catechism of the Catholic Church on the Holy Trinity
Catechism of the Catholic Church offers these words as an explanation of the Holy Trinity.
"The mystery of the Most Holy Trinity is the central mystery of the Christian faith and of Christian life. God alone can make it known to us by revealing Himself as Father, Son, and Holy Spirit."
"The Incarnation of God's Son reveals that God is the eternal Father and that the Son is consubstantial with the Father, which means that, in the Father and with the Father, the Son is one and the same God."
"The mission of the Holy Spirit, sent by the Father in the name of the Son (John 14:26) and by the Son: from the Father (John 15:26), reveals that, with them, the Spirit is one and the same God. "With the Father and the Son He is worshipped and glorified" (Nicene Creed)."
"Inseparable in what they are, the Divine Persons are also inseparable in what they do. But within the single divine operation each shows forth what is proper to Him in the Trinity, especially in the divine missions of the Son's Incarnation and the gift of the Holy Spirit."
-- Catechism of the Catholic Church §§ 261, 262, 263, 267