Tertullian is the guy who first used the term "Trinity" sometime in the early 200s. Tertullian's Trinity is unlike the one we have today. Rather than being "Three persons in one essence" his simply was a triad of three beings, two of which the Son and Holy Spirit were derived from the Father.
For a full academic treatment of the subject I recommend reading the StanFord University article that is linked below. In my previous posts, I did my best cover all the intellectual antecedents that led to the early Trinitarian theories some of which are not usually discussed even in Church History and Theology books and presentations (even the one listed below).
Trinity > History of Trinitarian Doctrines (Stanford Encyclopedia of Philosophy)
