The doctrine of the Trinity is encapsulated in Matthew 28:19, where Jesus instructs the apostles: "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit."
The first Christians, like the Jews before them, were fiercely monotheistic, willing to die horrible martyrs’ deaths in the Coliseum—being slain by gladiators, devoured by wild animals, crucified, or tied to a stake and turned into human torches—rather than concede the existence of any other gods.
This adamant insistence on monotheism is taken directly from the teaching of the Bible. Thus, in John 17:3 Jesus addresses his Father, saying, "And this is eternal life, that they know you—the only true God."
The early Christians were quick to spot new heresies. In the third century, Sabellius, a Libyan priest who was staying at Rome, invented a new one. He claimed there is only one person in the Godhead, so that the Father, the Son, and the Holy Spirit are all one person with different "offices," rather than three persons who are one being in the Godhead, as the orthodox position holds.
Certain groups, notably the Mormons, have committed the error of saying that God the Father has a body, and have thus become anthropomorphites, people who say that God has a human form.
In recent years, this form of doctrinal decay has also set in among certain segments of American Evangelicalism, most notably in the Pentecostal Word Faith movement. Evangelicals such as Finnis Dake, Jimmy Swaggart, Kenneth Copeland, and Benny Hinn have all (temporarily or permanently) bought into the idea that the Father has a body.
The Western Church commonly uses a version of the Nicene creed which has the Latin word filioque ("and the Son") added after the declaration that the Holy Spirit proceeds from the Father. Scripture reveals that the Spirit proceeds from the Father and the Son. The external relationships of the persons of the Trinity mirror their internal relationships. Just as the Father externally sent the Son into the world in time, the Son internally proceeds from the Father in the Trinity.
"Between heresy and schism there is this difference, that heresy perverts dogma, while schism, by rebellion against the bishop, separates from the Church. Nevertheless there is no schism which does not trump up a heresy to justify its departure from the Church."
~ St. Jerome, (In Ep. ad Tit., iii, 10), remarking on how practically and historically, heresy and schism nearly always go hand in hand.