The doctrine that the one God exists eternally as three distinct persons—the Father, Son and Holy Spirit—and each person is fully God.

• From the Bible:

  And when Jesus was baptized, immediately he went up from the water, and behold, the heavens were opened to him, and he saw the Spirit of God descending like a dove and coming to rest on him; and behold, a voice from heaven said, “This is my beloved Son, with whom I am well pleased.” (Matthew 3:16-17 ESV)

• From the Athanasian Creed:
  

  We worship one God in trinity and the Trinity in unity, neither confusing the persons nor dividing the divine being. For the Father is one person, the Son is another, and the Spirit is still another. But the deity of the Father, Son, and Holy Spirit is one, equal in glory, coeternal in majesty. What the Father is, the Son is, and so is the Holy Spirit. Uncreated is the Father; uncreated is the Son; uncreated is the Spirit. The Father is infinite; the Son is infinite; the Holy Spirit is infinite. Eternal is the Father; eternal is the Son; eternal is the Spirit: And yet there are not three eternal beings, but one who is eternal; as there are not three uncreated and unlimited beings, but one who is uncreated and unlimited. Almighty is the Father; almighty is the Son; almighty is the Spirit: And yet there are not three almighty beings, but one who is almighty. Thus the Father is God; the Son is God; the Holy Spirit is God: And yet there are not three gods, but one God. Thus the Father is Lord; the Son is Lord; the Holy Spirit is Lord: And yet there are not three lords, but one Lord.
  
  As Christian truth compels us to acknowledge each distinct person as God and Lord, so catholic religion forbids us to say that there are three gods or lords. The Father was neither made nor created nor begotten; the Son was neither made nor created, but was alone begotten of the Father; the Spirit was neither made nor created, but is proceeding from the Father and the Son. Thus there is one Father, not three fathers; one Son, not three sons; one Holy Spirit, not three spirits. And in this Trinity, no one is before or after, greater or less than the other; but all three persons are in themselves, coeternal and coequal; and so we must worship the Trinity in unity and the one God in three persons. Whoever wants to be saved should think thus about the Trinity.

• From J.I. Packer in Concise Theology: 

  The practical importance of the doctrine of the Trinity is that it requires us to pay equal attention, and give equal honor, to all three persons in the unity of their gracious ministry to us. That ministry is the subject matter of the gospel, which, as Jesus’ conversation with Nicodemus shows, cannot be stated without bringing in their distinct roles in God’s plan of grace (John 3:1-15; note especially vv. 3, 5-8, 13-15, and John’s expository comments, which NIV renders as part of the conversation itself, vv. 16-21). All non-Trinitarian formulations of the Christian message are by biblical standards inadequate and indeed fundamentally false, and will naturally tend to pull Christian lives out of shape.

1. James White: A Brief Definition of the Trinity
2. GotQuestions.org: What does the Bible teach about the Trinity?
3. Tim Challies: The Essential Trinity
4. J. I. Packer: Trinity
5. Desiring God staff: What is the doctrine of the Trinity?
6. R. Scott Clark: The Splendor of the Three-In-One God: The Necessity and Mystery of the Trinity
7. Tim Challies: Visual Theology - The Trinity (infographic)
8. Wayne Grudem: The Doctrine of the Trinity: part 1, part 2, part 3, part 4 (mp3s)
9. J. I. Packer: The Trinity - Part 1, The Trinity - Part 2 (mp3s)
10. James White: The Trinity Defended 1, The Trinity Defended 2 (mp3s)

• economic Trinity
• ontological Trinity
• hypostatic union
• person
• being

• Quiz on the Biblical and Historical Doctrine of the Trinity
• Answers to Quiz on the Trinity