Very little is known about Athenagoras except that he was a Christian and a philosopher.

That we are not atheists, therefore, seeing that we acknowledge One God, uncreated, eternal, invisible, impassible, incomprehensible, illimitable, who is apprehended by the understanding only and the Reason, who is encompassed by light, and beauty, and spirit, and power ineffable, by whom the universe has been created through His Word, and set in order, and is kept in being, I have sufficiently demonstrated. [I say "His Logos"], for we acknowledge also a Son of God. Nor let any one think it ridiculous that God should have a Son. For though the poets, in their fictions, represent the gods as no better than men, our mode of thinking is not the same as theirs, concerning either God the Father or the Son. But the Son of God is the Word of the Father, in idea and in operation, for after the pattern of him and by him were all things made, the Father and the Son being one. And, the Son being in the Father and the Father in the Son, in oneness and power of Spirit, the knowledge and Word of the Father is the Son of God. But if, in your surpassing intelligence, it occurs to you to inquire what is meant by the Son, I will state briefly that He is the first product of the Father, not as having been brought into existence (for from the beginning, God, who is the eternal mind [nous], had the Logos in Himself, being from eternity instinct with Word, but inasmuch as He came forth to be the idea and energizing power of all material things, which lay like a nature without attributes, and an inactive earth, the grosser particles being mixed up with the lighter. The prophetic Spirit also agrees with our statements. "The Lord," it says, "made Me, the beginning of His ways to His works." The Holy Spirit Himself also, which operates in the prophets, we assert to be an effluence of God, flowing from Him, and returning back again like a beam of the sun. Who, then, would not be astonished to hear men who speak of God the Father, and of God the Son, and of the Holy Spirit, and who declare both their power in union and their distinction in order, called atheists? Nor is our teaching in what relates to the divine nature confined to these points; but we recognise also a multitude of angels and ministers, whom God the Maker and Framer of the world distributed and appointed to their several posts by His Word, to occupy themselves about the elements, and the heavens, and the world, and the things in it, and the goodly ordering of them all." (A Plea for the Christians, 10).

If one reads this carefully, we can see he begins this exposition by referring to the "One God." There is no doubt that Athenagoras clearly understands the "One God" to be both the Creator and the Father of Jesus Christ and in this way he distinguishes between the "One God" and "the Son." For Athenagoras, and his contemporary Christian brethren, Jesus was divine but not God by identity. His divinity was a derivation of God's divinity like the sunbeam of the sun, he was the light of The Light, a manifestation of God but not the One God himself. The Word/Logos is described as "His" Word/Logos, that is, the one God's Word/Logos. Since the One God's Word has his quality because it came from him, begotten out of Him, then the Son is the quality of God, yet not the One God himself by identity. He also equates the phrase "Word/Logos of the Father" with the term "Son of God" thereby indicating the Son is not God but "of" God. He also explains how the Father and the Son are one; they are one in the Spirit. In other words, this is their common nature and the means by which they share common divinity. Yet, we must also understand that Athenagoras is not speaking of the Son in terms of his incarnation where he emptied himself out of Spirit to become flesh. Athenagoras describes the Son as the first product of the Father but makes it clear that he does not want to be misunderstood on this matter and goes on to explain that the Son is not a created being but was begotten out of the One Unbegotten God. Essentially what he is saying here is that creation came out of the Word/Logos but the Word/Logos came out of God the Father where he had eternally existed prior to God begetting his Word. In other words, the Son is out of the unbegotten God. He then goes on to explain that the Father, the Son, and the Holy Spirit have a distinction in order and goes one step further and attributes divine nature to the angels as well (see Heb 1:14). He explains that the angels are ordered by the power of the Word/Logos, that is, the Son, or Jesus Christ.

Athenagoras also does not personify the Spirit but describes the Spirit as an effluence or effulgence or emanation of God.

Athenagoras most definitely would not agree with the later formulation of the Trinity which describes the Father and the Son and the Holy Spirit as the "one God." In Athenagoras' mind, the Son was "of" the Father and "of" the One God because of derivation from that One God. He did not fall prey to the later Trinitarian false premise that to share the nature of the one God, or to be uncreated, was to qualify as actually being that One God by identity.