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Until the third century, the dichotomy of trinitarians and non-trinitarians just did not exist. Jesus was the Son of God, and that was as far as it went. The concept of the Trinity began to provide for the divinity of Jesus within a monotheistic framework. Around the beginning of the fourth century, a Libyan priest, Arius, began to teach that the Trinity was wrong - Jesus, the Son of God, was not co-eternal and consubstantial with his Father, but was rather a created being, subordinate to the Father. Bishop Alexander of Alexandria excommunicated Arius and had the Council of Nicaea declare for the Trinity. However, the Christian world remained divided on the issue until Emperor Theodosius made belief in the Trinity mandatory for Christians at the end of the fourth century. Throughout much of the fourth century, it remained possible, in spite of successive ecumenical councils, that Arianism would win the day and that it would be Trinitarianism that would be declared heretical.
In terms of number of adherents, nontrinitarian denominations comprise only a small minority of modern Christianity. By far the two largest nontrinitarian denominations are The Church of Jesus Christ of Latter-day Saints ("Mormons") and the Jehovah's Witnesses. According to Wikipedia, other denominations include the Christadelphians, Christian Scientists, Dawn Bible Students, Friends General Conference, Iglesia ni Cristo, Living Church of God, Oneness Pentecostals, Members Church of God International, Unitarian Universalist Christians, The Way International, The Church of God International and the United Church of God. Nontrinitarian views differ widely on the nature of God, Jesus and the Holy Spirit. Some important nontrinitarian views are:
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There is a range of views and the Christology of each view can be quite complicated, but here is a potted version of some of them:
In the early 19th century, Unitarian Robert Wallace identified three particular classes of Unitarian doctrines in history: Arians, which believed in a pre-existence of the divine spirit, but maintained that Jesus was created and lived as human only; "Socinians", which, denied his original divinity, but agreed that Christ should be worshipped; and "Strict unitarians", which, believing in an "incommunicable divinity of God", denied both the existence of the Holy Spirit and the worship of "the man Christ." - https://en.wikipedia.org/wiki/Unitarianism#Christology