Having said in the previous two posts that Unitarianism has its roots in Christianity, we must ask: in what kind of Christianity does it have roots?
It is the heir of Renaissance humanism; of Anabaptists, Socinians, Arians, Lollards, Universalists, Arminians, and other liberal and heretical schools of thought. And it is the child of Enlightenment Deism, and of Enlightenment thought generally.
In ancient Greece, a haeresis was a school of thought, and diversity of ideas was considered valuable; it was only in the Christian era that a definitive version of truth was thought desirable and so heresy became anathema.
The Renaissance humanists were the first to campaign for education in the humanities (grammar, rhetoric, history, poetry and moral philosophy), and to improve the understanding and translations of Biblical and early Christian texts, as well as translating classical pagan texts. Unitarianism has, for most of its history as a movement, been keen on biblical criticism, and using one's reason to work out what the texts mean (not relying on external authority for an interpretation).
The Arian heresy, first propounded at the Council of Nicaea in 325 CE, is the view that Christ is not "very God of very God" - he is either God's son by adoption or by creation. The Arian concept of Christ is that the Son of God did not always exist, but was created by — and is therefore distinct from and inferior to — God the Father. This being so makes him no longer unique, and also has implications for other Christian doctrines.
The Socinians held an Arian view of Christ, and it is arguably they who discovered the principle of tolerance which is such an important part of Unitarian values. At one of their earliest church councils, they discovered that they could not agree on several theological points — so they agreed to differ, rather than create further schism. The Socinians emerged from among the Anabaptists of Northern Italy in the late 16th century; Fausto Sozzini, their founder, had read the works of Servetus on the errors of the Trinity. When they arrived in Poland, the Socinians started a printing press at Rakow (which town was subsequently razed to the ground by the Catholics) and from Rakow, Socinian and Unitarian ideas spread to England and Transylvania — where, in due course, the Polish Socinians fled, as Poland was caught in the grip of the Counter-Reformation. In due course the Unitarians of Transylvania became a church which still survives today, and Unitarianism was founded in England by Joseph Priestley and Theophilus Lindsey.
The Lollards do not, as far as I know, have any direct connection with Unitarianism, but they are interesting as the first group to have translated the Bible into English, and to have looked outside the Catholic Church for the source of religious authority. Some of them were thought to have been non-trinitarians.
The Universalists never formed a formal church in England (although the General Baptists, who were much influenced by Arminianism, did reject the Calvinist doctrine of predestination, and most General Baptist churches joined the Unitarian movement and retain a distinct identity within it). However, the idea of universal reconciliation was popular in England, and was held by many Unitarians, who also rejected vicarious atonement.
Many early Unitarians believed in "salvation by character" and so were interested in books like The Imitation of Christ. So it seems that they drew on mystical and contemplative forms of Christianity as well as the liberal and rational Protestant forms mentioned above. Many Unitarian churches started out as liberal Presbyterian; others were Independents.
But the most important aspect of Unitarianism for me is that it is reasonable, and tolerant, and honours diversity. The famous Unitarian values of freedom, reason and tolerance are said to have emerged because people wanted the freedom to reason about what the Bible meant; but then they found that different people came to different conclusions about what it meant, so then they had to tolerate each others' different opinions. Unitarians have never burnt anyone at the stake or killed them for their beliefs. On the contrary, Unitarians have frequently been killed or burnt for their beliefs.
Another massively important aspect of Unitarianism is its positive attitude to other faiths, which stems partly from the idea that Jesus is an exemplar and not a saviour — if he is not a saviour, there is no need to convert people of other faiths to Christianity; and because Unitarians believe that the Divine reveals itself to different peoples in different ways, other religions are respected (though might be criticised for harmful practices).
The Unitarian insistence on building the Kingdom of Heaven on Earth also appeals to me. And of course the fact that it is inclusive of LGBT people, and has always campaigned for the education and emancipation of women, the abolition of slavery, and social justice generally, is really important. And so is its positive attitude to science. Charles Darwin was the son of a Unitarian, and his wife Emma was a Unitarian as well. Unitarians were probably among the earliest to accept evolution — certainly Barbara Bodichon (Unitarian and Pre-Raphaelite) had accepted it, as she painted controversial geological views of cliffs.
Modern Unitarianism has also been profoundly influenced by Transcendentalism, which grew out of 19th century American Unitarianism, and also influenced the Pagan revival, and much of American and European life and literature. I have written elsewhere on how Ralph Waldo Emerson, and hence Transcendentalism, was influenced by the translation of the Upanishads into English by Rammohun Roy, founder of the Brahmo Samaj and campaigner for the education of women and the abolition of sati. The Transcendentalists believed (among other things) in an ideal spirituality that "transcends" the physical and empirical and is realized only through the individual's intuition, rather than through the doctrines of established religions.
So these are the kind of ideas of which Unitarianism is the heir — not the narrow and pessimistic doctrines of Calvinists, Evangelicals and scholasticism, but the broad and tolerant strains of the Reformation, which sought freedom and tolerance. The systems of thought which were the forerunners of Unitarianism were optimistic about human and divine nature. They were not world-denying, but world-affirming.