What is God's nature in simplest terms? What essential principles governs how God interacts within the trinity and with his creation?
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The simplest terms? There can be only one answer, I think:
This is the very heart of who the Christian God is. To answer the second part of your question; it defines how He interacts within the Trinity1:
and with His creation:
1It also shows why there has to be a Trinity. God cannot be love if He is just one Person. Instead, it requires one Person to love Another, and that Love between them is Another (source and also Romans 5:5).
This, being not a philosophy site where all possible natures are to be debated, I will endeavor to simply state the most fundamental ways in which Christianity knows to describe God. This is, at best, a nearly futile exercise, but we have been given a few guides. First as an illustration of how words will never do him justice, note how he chooses to introduce himself:
No explanation. No description. No more. Just "I AM".
However, he doesn't leave us hanging. Most significantly, the "I AM" revealed himself in both time and space in the person of Jesus Christ, "The image of the invisible God". Through him we catch a glimpse of God, and through his own teachings and affirmations of the OT scriptures we arrive at various ways of expressing what sort of thing God is.
Likewise we know much about his works, that in turn tell us more about what he is. For example, we know he is the creator of all things. This is referenced many times in Scripture, but here is the corresponding statement from the Nicene Creed, one of the basic statements about what Christians believe.
Likewise we also know some things about his Character which help fill out the picture. For example we know that he is able to have personal relationships and what characteristics he shows in those relationships.
Yet "love" is just one of his attributes. It is hard to say what is most fundamental about him, but if anything, the only attribute that is constantly emphasized by being repeated three times, would be his holiness.
From this (and many other Scriptures) we get the idea of a perfect God who transcends many of our measurable attributes like time or space, yet who interacts with physical creation and carries on a relationship with those he has made.
A more detailed statement comprised of information from many parts of Scripture can be found in the many Creeds and Confessions, such as this except from the Westminster Confession:
It would be remiss to touch on this subject without also mentioning the Trinity. God as he has revealed himself to us is but one being yet he has three persons by which we know him. Again we arrive at this picture through a multitude of references and the words of Jesus himself, yet it is very hard to put into words. One of the most valiant attempts I know of is The Athanasian Creed, excerpted:
In His own words:
And in centuries of sudy, we still only have a surface understanding of what that means, who He is, and his essence. We have, from Scripture, everything we need to understand what He wants us to know about Him, but even in a lifetime of study, our understanding changes somewhat with each pass through the Bible.