There is one God, who eternally exists as three Persons: Father, Son, and Holy Spirit, the same in essence, distinct in Person. Scripture does not give this as a philosophy; it shows it in the life of God revealed in Christ and in the work of salvation.
Not a summary of these passages: the passages themselves. Read them, then come back to the study below.
The study
What the Scripture says
1
There is one God
Scripture is emphatic: 'Hear, Israel: Yahweh is our God. Yahweh is one.' God declares, 'I am Yahweh, and there is no one else.' The Bible is fiercely monotheistic: there is one God, and nothing else is to be worshipped.
The Father is God; the Son is called God: 'In the beginning was the Word, and the Word was with God, and the Word was God,' and Thomas confesses Jesus as 'My Lord and my God'; and the Spirit is God, as Peter made plain to Ananias. Three Persons, each fully divine.
In the beginning was the Word, and the Word was with God, and the Word was God.
But Peter said, “Ananias, why has Satan filled your heart to lie to the Holy Spirit, and to keep back part of the price of the land? While you kept it, didn’t it remain your own? After it was sold, wasn’t it in your power? How is it that you have conceived this thing in your heart? You haven’t lied to men, but to God.”
Yet they are distinct Persons who relate to one another
At Jesus' baptism, the Spirit descends upon the Son while the Father speaks from heaven: three Persons present at once. In the upper room, the Son asks the Father to send the Spirit. They love, send, glorify, and speak to one another.
Jesus, when he was baptized, went up directly from the water: and behold, the heavens were opened to him. He saw the Spirit of God descending as a dove, and coming on him. Behold, a voice out of the heavens said, “This is my beloved Son, with whom I am well pleased.”
I will pray to the Father, and he will give you another Counselor, that he may be with you forever,— the Spirit of truth, whom the world can’t receive; for it doesn’t see him, neither knows him. You know him, for he lives with you, and will be in you.
Jesus said these things, and lifting up his eyes to heaven, he said, “Father, the time has come. Glorify your Son, that your Son may also glorify you; even as you gave him authority over all flesh, he will give eternal life to all whom you have given him. This is eternal life, that they should know you, the only true God, and him whom you sent, Jesus Christ. I glorified you on the earth. I have accomplished the work which you have given me to do. Now, Father, glorify me with your own self with the glory which I had with you before the world existed.
The Great Commission puts it beyond dispute: baptize 'in the name,' singular, 'of the Father and of the Son and of the Holy Spirit.' The earliest confession of the church was already trinitarian, because that is how God revealed Himself.
Go,and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
The Father chose us and loved us before the foundation of the world; the Son redeemed us by His blood; the Spirit sealed us and dwells in us. Every blessing of salvation flows from the triune God, and we are invited into His fellowship.
Blessed be the God and Father of our Lord Jesus Christ, who has blessed us with every spiritual blessing in the heavenly places in Christ; even as he chose us in him before the foundation of the world, that we would be holy and without defect before him in love; having predestined us for adoption as children through Jesus Christ to himself, according to the good pleasure of his desire, to the praise of the glory of his grace, by which he freely bestowed favor on us in the Beloved, in whom we have our redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace, which he made to abound toward us in all wisdom and prudence, making known to us the mystery of his will, according to his good pleasure which he purposed in him to an administration of the fullness of the times, to sum up all things in Christ, the things in the heavens, and the things on the earth, in him; in whom also we were assigned an inheritance, having been foreordained according to the purpose of him who works all things after the counsel of his will; to the end that we should be to the praise of his glory, we who had before hoped in Christ: in whom you also, having heard the word of the truth, the Good News of your salvation—in whom, having also believed, you were sealed with the Holy Spirit of promise, who is a pledge of our inheritance, to the redemption of God’s own possession, to the praise of his glory.
I will pray to the Father, and he will give you another Counselor, that he may be with you forever,— the Spirit of truth, whom the world can’t receive; for it doesn’t see him, neither knows him. You know him, for he lives with you, and will be in you.
His Son is the radiance of his glory, the very image of his substance, and upholding all things by the word of his power, when he had by himself purified us of our sins, sat down on the right hand of the Majesty on high;