I'm probably oversimplifying here, but as far as I understand there are primarily two universalists. First, more commonly, the ones that believe that Christ's atonement covered all people, regardless of specific acknowledgement of those beliefs. Second, less common, the more mystical interpretation of the Bible that the Good News is pointing to perennial truths...i.e. that Jesus was teaching and pointing to humanity's birthright. Mystical Christians see "Christ" through a lens of a more universal spiritual energy that applies to all humanity.
Traditional Universalism - the "all" passages. There are many verses in the Bible that refer to a universal reconciliation to God via the use of the word all.
>"For as in Adam all die, even so in Christ shall all be made alive." (1 Cor 15:22)
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>"And all people will see God’s salvation." (Luke 3:6)
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>"Consequently, just as one trespass resulted in condemnation for all people, so also one righteous act resulted in justification and life for all people."
Good references:
https://campuspress.yale.edu/keithderose/1129-2/#3 (Professor of Philosophy from Yale)
That All Shall Be Saved (David Bentley Hart) (perhaps the most mentioned book I've come across regarding the claim of Universalism as Biblical)
Mystical Universalism - This is a view in Christianity that all will ultimately be united with God. The key difference is that mystics tend to honor and celebrate all paths as leading to God. They read and interpret the Biblical text as pointing to perennial truths that overlap in all the major world religions and spiritual traditions.
Verses:
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"On that day you will realize that I am in my Father, and you are in me, and I am in you." (John 14:20)
"The kingdom of God does not come with observation; nor will they say, ‘See here!’ or ‘See there!’ For indeed, the kingdom of God is within you” (Luke 17:20-21)
Good references:
Anything written by Richard Rohr. Perhaps The Universal Christ as one option, but really Rohr's teaching is consistent. Also, check him out on Youtube. A great synopsis of his teaching can be found there.