Book I. The treatise begins with St. Hilary's own spiritual history, the events of which are displayed, no doubt, more logically and symmetrically in the narrative than they had occurred in the writer's experience. He tells of the efforts of a pure and noble soul, impeded, so far as we hear, neither by unworthy desires nor by indifference, to find an adequate end and aim of life. He rises first to the conception of the old philosophers, and then by successive advances, as he learns more and more of the Divine revelation in Scripture, he attains the object of his search in the apprehension of God as revealed in the Catholic Faith.
But this happiness is not the result of a mere intellectual knowledge, but of belief as well. In §§ 1-14 we have this advance from ignorance and fear to knowledge and peace. And here he might have rested, had he not been charged with the sacerdotal (i.e., in the language of that time, the episcopal) office, which laid upon him the duty of caring for the salvation of others. And such care was needed, for (§§ 15, 16) heresies were abroad, and chiefly two; the Sabellian which said that Father and Son were mere names or aspects of one Divine Person, and therefore there had been no true birth of the Son; and the Arian (which, however, Hilary rarely calls by the name of its advocate, preferring to style it the 'new heresy') asserting more or less openly that the Son is created and not born, and therefore is different in kind from the Father, and not, in the true sense, God.
Hilary declares (§ 17) that his purpose is to refute these heresies and to demonstrate the true faith by the evidence of Scripture. He demands from his hearers a loyal belief in the Scriptures which he will cite; without such faith his arguments will not profit them (§ 18); and in § 19 he warns them of the limits of the argument from analogy, which he must employ, inadequate as it is in respect of the finite illustrations which he must use to express the infinite. Then in § 20 he speaks with a modest pride of his careful marshalling of the arguments which shall lead his readers to the right conclusion, and in §§ 21-36 he gives a summary of the contents of the work.
He concludes the first Book (§§ 37, 38) with a prayer which expresses his certainty that what he holds is the truth, and entreats the Father and the Son that he may have the eloquence of language and the cogency of reasoning needed for the worthy presentation of the truth concerning Them.
Source: On the Trinity (New Advent)