The Trinity is never mentioned by that name in the Bible. While God, Jesus, and the Holy Spirit are all mentioned separately throughout the New Testament, there is only one passage which provides support for Trinitarian doctrine: 1 John 5:7-8 , which scholars call the Johannine Comma:
7 For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.
8 And there are three that bear witness in earth, the Spirit, and the water, and the blood: and these three agree in one.
This passage, the only Biblical support for the Trinitarian doctrine, is not found in the oldest and best Greek manuscripts of the New Testament, which instead read "These are three that bear witness: the Spirit, the water, and the blood, and these three are one." Scholars believe the Johannine Comma to be a later addition to the New Testament, inserted to justify the doctrines of the orthodoxy.
There have been a wide variety of different interpretations of the nature of the Trinity over the centuries. Modalism is an early Christian view that suggests that the three entities are different forms of a single God, in much the same way that water has solid, liquid, and gaseous forms. While some churches retain a modalistic interpretation, orthodox Trinitarians consider it to be heresy. Unitarians deny the Trinity altogether, believing that there is one God, and that Jesus was merely a human prophet or perhaps a supernatural entity in his own right, but was not God in the flesh. Arianism was an early Christian doctrine which claimed that Jesus was created by God the Father, who later worked through Jesus to create the Holy Spirit, setting up a hierarchical godhead of separate entities. The Arian Controversy was a major reason for the Council of Nicea, which defined the Christian orthodoxy and effectively declared Arianism heretical. The Mormons believe that God, Jesus, and the Holy Spirit are separate entities with separate bodies, united in single purpose.