In the fourth chapter in Can These Bones Live?, Robert W Jenson has an excellent biblical theological overview of the Trinity.
Jenson begins by tracing the historic development of the doctrine of the Trinity. Historically, the doctrine of the Trinity was solidified through the Nicene Creed; it was further grounded by the Cappadocian fathers. Jenson summarizes the historical articulation of the Trinity by explaining the difference between being and person or hypostases: “There is in God… just one being, which is why there is just one God. The is-ness of God is single, but there are three hypostases [or persons]” (p 48). So then, Christians worship one God who eternally exists in three persons. Jenson concludes that this is “the most biblical view” (p 48).
But of course, in order for it to be the most biblical view, it must be found in the Bible. The question then becomes, can the Trinity be found in the Bible? Or is the Trinity a novel doctrine created by the early Christians? Jenson explains:
It is often supposed that Christian trinitarianism is a total break from Judaism’s understanding of God. The Jews are said to have the doctrine that there is only one God and the Christians are said to have introduced a modification. This is historically false, and two of the most profound contemporary Jewish theologians, Michael Wyschogrod and Peter Ochs, both recognize that. Neither Judaism nor Christianity is an abstract monotheist religion. Neither insists that there is just one God and that this is all that can be said about him. Both are rather instances of what I would like to call “dramatic monotheism.” For both Judaism and Christianity, the oneness of God is the oneness of the story that he lives with his people. (p 48-49)
Jenson then goes on to explain that the OT presents a dramatic God who not only exists outside of history as “its author, who in some sense stands outside of the play or drama as the author of the drama” (p 49), but also…
as a figure in the drama, a figure in the history of Israel. Consider, for example, “the angel of the Lord.” Throughout the Pentateuch when something really decisive happens, the “malach yhwh”— that is, the angel or messenger of the Lord— appears to speak on the Lord’s behalf. As the tale goes on, however, this angel or messenger of the Lord speaks as God in the first person. It turns out that he is the Lord. So the malach of the Lord is simultaneously a messenger for the Lord or of the Lord but also the Lord himself. (p 49)
Jenson also points out the glory cloud of the Lord that is understood to be the presence of the Lord himself:
In the temple of Jerusalem we find simultaneously a manifestation of the Lord, the glory of the Lord, and a sort of shining of the Lord which just is the Lord…
The old rabbis of somewhere between 150 bc to ad 300 regarded such phenomena as different forms of the same thing which they called the “shekinah,” which means “the settlement one” or “the resident one.” The shekinah of God, then, is God as resident within the life of Israel as distinguished from God as author and transcendent to the life of Israel. (p 49-50)
Jenson notices “there are three” persons who are generally equated as YHWH in the OT, each in some way participating within the drama of Israel. This leads to the conclusion that the YHWH of Israel is more dynamic than simply one God as one person.
When this drama turns to the NT, Jenson observes that for the writers of the NT letters, the resurrection of Christ came to mean that the Shekinah glory of the temple had come to illumine and dwell within one man, a single Israelite (p 50). No longer was the glory outside of the people, but it had come to make its home within mankind. Even more then that, it is said in the NT that it was the Father who raised Jesus by the power of the Shekinah. Thus, the NT continues the threeness of the OT: the Son was raised by the Father in the power of the Spirit.