The language of the ancient Fathers and Councils was primarily that God is one Ousia and three Hypostases. Which is why in the Nicene Creed we confess that the Son is ὁμοούσιον (homoousion) with the Father, literally "of-the-same-Being".
The word ousia is the noun form of the Greek verb meaning "to be", so literally translated to English as "being", or in Latin as essentia from which we get the word "essence" (this, also from the Latin verb for "to be" esse). We also translate this word as "substance", from the Latin substantia.
The word hypostasis is a bit more complicated, it can be literally translated as "substance", as it is hypo (under or Latin sub) and stasis (to stand or stancia in Latin); but theologians have preferred to render it as "subsistence". One could literally translate the word to "understanding", but that could be confusing to an English speaker. The meat of the meaning of this word is that we are speaking of something concrete and real, so when we speak of the "Hypostasis of the Father" we are speaking of the Father's "Father-ness", He is real, distinct, actual and not to be confused with the Son and the Holy Spirit. And yet the Son and the Holy Spirit are (by the eternal generation of the Son and the eternal procession of the Holy Spirit respectively) of the same Being as the Father, i.e. God, the one and only God.
So the Three Hypostases are one in Ousia. The Father is God, the Son is God, and the Holy Spirit is God; not three gods, but one God; not three eternals, but one Eternal; not three almighties, but one Almighty. Etc.
Another important word here is the Greek prosopon (plural: prosopa), which is translated directly into Latin as persona (plural: personae), from which the English word "person" is derived. The word had, in antiquity, a number of problems and controversies surrounding it. As a literal translation of prosopon would be "face" or "mask"; in traditional Greek theater actors would wear masks (prosopa) to play their role in the play. As such, this term was used by the ancient Modalists to say that God was one Hypostasis who wore three different faces. This was rejected as heretical, because it denied the reality and the actual distinction between the Father, Son, and the Holy Spirit by diminishing them to mere faces or masks which God wore. However, the word prosopon (and persona in Latin) was used again later on as another way of speaking of the distinct Hypostases of the Trinity.
It is in this sense, not as "masks", but as Hypostases-Prosopa, that in English we speak of the Three Divine Persons. By which we mean real, distinct, concrete, "Someones"; not God wearing different faces, or three divine beings. But the Three Someones who are, each unto Himself and in/with the Other is truly God, the one God. The Being, the Essence, the Godhood of the Father is the same Being, the same Essence, the same Godhood of the Son and the Holy Spirit. Thus the Father is the one and only God, the Son also is the one and only God, and the Holy Spirit is the one and only God.
The Father is God, begotten of none; the Son is God, begotten of the Father; the Holy Spirit is God, proceeding from the Father [and the Son]. So that we confess, believe in, and worship "one God in Trinity, and Trinity in Unity, neither confusing the Persons nor dividing the Essence" as we read in the Athanasian Creed.
This is the Doctrine of the Trinity as it has been confessed and believed down through the generations; with its origins in the biblical confession of the one God and the Three Divine Persons.
So that when the Scriptures declare, "Hear O Israel, YHWH our God, YHWH is one" (Deuteronomy 6:4) and "Go and make disciples of all nations, baptizing them in the Name of the Father, Son, and the Holy Spirit" (Matthew 28:19) there is no contradiction. For the one and undivided God YHWH bears the singular Name of Father, Son, and Holy Spirit. When we read of our Lord Jesus, therefore, saying, "Before Abraham was I AM" (John 8:58) there is no doubt as to why His hearers accused Him of blasphemy. Jesus declared to be the One and singular God, YHWH, the One who said to Moses, "I AM that I AM"; and this same Jesus also deferred to His Father, and could say, "I go to My God and to your God" (John 20:17). For the Father, who is I AM, has a Son who is I AM, and the Holy Spirit is I AM. The one God of Deuteronomy 6:4 is also the Three Persons of Father, Son, and Holy Spirit.
For even as the Father has life in Himself, so does the Son (John 5:26), as the Son being the express image of the Father's Hypostasis (Hebrews 1:3) is confessed as true and very God, "Your Throne O God is forever and ever" (Hebrews 1:8). And the Son Himself, says that He and His Father will send Another Helper, the Holy Spirit, distinct from Father and the Son, and yet also Christ says of the Spirit, "I will not leave you as orphans, I will come to you" (John 14:18).
So in "Hear O Israel, YHWH our God" the Christian Church, through the revelation we have received in Christ, knows this one God as the Father, Son, and the Holy Spirit. For this reason, again, the Church believes in, confesses, and worships the "one God in Trinity, Trinity in Unity, neither confusing the Persons nor dividing the Essence." Amen.
-CryptoLutheran