Introduction

There are some faith traditions which denounce the Holy Trinity as polytheistic. As Catholics, we confess our belief in one God at every mass. A great mystery of our faith is that God is of one essence, but who revealed Himself in three persons. These three persons are the Father, the Son and the Holy Spirit. If we could fit this mystery of God into our intellect then He would not be God. Why is this so? Because it would mean that our infinite God was finite. The existence of mystery in our faith is not a stumbling block, but rather a testimony that we believe in a great God, and not something devised by man. However, it is helpful to look at analogies just as our Lord used parables to illuminate these mysteries. Think of our rising sun as God the Father. Think of its light as the Son of God. Think of its warmth as the Holy Spirit. The sun lends its existence to the light that was begotten of it. The heat can proceed from the light, and from the body of the sun itself. Therefore, like the Holy Trinity, each of these is perceived by us distinctly, yet they are indivisible.

Catechism
The Trinity is One. We do not confess three Gods, but one God in three persons, the "consubstantial Trinity". The divine persons do not share the one divinity among themselves but each of them is God whole and entire: "The Father is that which the Son is, the Son that which the Father is, the Father and the Son that which the Holy Spirit is, i.e. by nature one God."
- Catechism of the Catholic Church, 2nd ed., (1997), n.253
The divine persons are relative to one another. Because it does not divide the divine unity, the real distinction of the persons from one another resides solely in the relationships which relate them to one another: "In the relational names of the persons the Father is related to the Son, the Son to the Father, and the Holy Spirit to both. While they are called three persons in view of their relations, we believe in one nature or substance." Indeed "everything (in them) is one where there is no opposition of relationship. Because of that unity the Father is wholly in the Son and wholly in the Holy Spirit; the Son is wholly in the Father and wholly in the Holy Spirit; the Holy Spirit is wholly in the Father and wholly in the Son."
- Catechism of the Catholic Church, 2nd ed., (1997), n.255
Scripture

Gen. 1:26 - God says Let us make man in our image. God is of one essence, but three persons.

Gen. 3:22 - God says man has become like one of us. The plural form is again used in referring to the persons of God.

Ex. 20:2-3 - I am the LORD your God [Elohim], …You shall have no other gods [Elohim] before Me.

Isa. 9:6 - The Father is God. He will have a Son(Jesus Christ) and a Counselor(Holy Spirit).

Isa. 48:16 - In the Old Testament, the nature of God is expressed as three persons in one God.

Jn. 1:1 - The Word is God. The Word is another name for Jesus Christ. This affirms Jesus is God.

Acts. 5:3-4,9 - The Holy Spirit is God. Peter says Ananias lied to the Holy Spirit…not to men, but to God (the Holy Spirit).

1 Jn. 5:7 - In the New Testament, the nature of God is expressed as three persons in one God.

Tradition & Fathers
"Having first said all these things, baptize into the name of the Father, and of the Son, and of the Holy Spirit..."
- Didache Apostolorum (A.D. ~90)
"… having learned that He[Jesus] is the Son of the true God Himself, and holding Him in the second place, and the prophetic Spirit in the third, we will prove."
- St. Justin Martyr, First Apology (A.D. ~110-165)
"Wherefore also I praise Thee for all things, I bless Thee, I glorify Thee, along with the everlasting and heavenly Jesus Christ, Thy beloved Son, with whom, to Thee, and the Holy Ghost, be glory both now and to all coming ages. Amen."
- Martyrdom of Polycarp (A.D. 157)
"For with Him were always present the Word and Wisdom, the Son and the Spirit, by whom and in whom, freely and spontaneously, He made all things, to whom also He speaks, saying, 'Let Us make man after Our image and likeness;' He taking from Himself the substance of the creatures [formed], and the pattern of things made, and the type of all the adornments in the world."