The doctrine of the Trinity coalesced intellectually during the course of the 4th century, but its roots go back to the theological musings of the earliest Christians, as preserved in the New Testament.  This is reflected in the first letter to Serapion by Athanasius, the great bishop of Alexandria.  It can be found in PG 26, 594-595, 599 (Ep 1 ad Serapionem, 28-30).

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We acknowledge the Trinity, holy and perfect, to consist of the Father, the Son and the Holy Spirit.  In this Trinity there is no intrusion of any alien element or of anything from outside, nor is the Trinity a blend of creative and created being.  It is a wholly creative and energizing reality, self-consistent and undivided in its active power, for the Father makes all things through the Word and in the Holy Spirit, and in this way the unity of the holy Trinity is preserved.  Accordingly, in the Church, one God is preached, one God who is above all things and through all things and in all things.  God is above all things as Father, for he is principle and source; he is through all things through the Word; and he is in all things in the Holy Spirit. 

Writing to the Corinthians about spiritual matters, Paul traces all reality back to one God, the Father, saying:  Now there are varieties of gifts, but the same Spirit; and varieties of service, but the same Lord; and there are varieties of working, but it is the same God who inspires them all in everyone.

Even the gifts that the Spirit dispenses to individuals are given by the Father through the Word.  For all that belongs to the Father belongs also to the Son, and so the graces given by the Son in the Spirit are true gifts of the Father. Similarly, when the Spirit dwells in us, the Word who bestows the Spirit is in us too, and the Father is present in the Word.  This is the meaning of the text:  My Father and I will come to him and make our home with him.  For where the light is, there also is the radiance; and where the radiance is, there too are its power and its resplendent grace.

This is also Paul's teaching in his second letter to the Corinthians:  The grace of our Lord Jesus Christ and the love of God and the fellowship of the Holy Spirit be with you all.  For grace and the gift of the Trinity are given by the Father through the Son in the Holy Spirit.  Just as grace is given from the Father through the Son, so there could be no communication of the gift to us except in the Holy Spirit.  But when we share in the Spirit, we possess the love of the Father, the grace of the Son and the fellowship of the Spirit himself.