Trinity, Oneness and The Persons of the Godhead

[Vic]

From Hope Secure:

Quote:I was in the public library one day reading at a table, minding my own business, and a young man sat down at the same table, he said what are you reading. It was Law and Grace by A J. McClain. He said I do not believe in the doctrine of the Trinity but the oneness doctrine. I explained that 3 Persons in 1 God was my belief. I had not heard of the oneness doctrine until then.

So the question is---what is the difference between the different views? What is Oneness doctrine? and What does the Bible say about all this?