1. Pelagianism is a theological theory named after Pelagius (AD 354 – AD 420/440), although he denied, at least at some point in his life, many of the doctrines associated with his name. It is the belief that original sin did not taint human nature and that mortal will is still capable of choosing good or evil without special Divine aid. This is still sometimes called Limited Depravity. Thus, Adam's sin was "to set a bad example" for his progeny, but his actions did not have the other consequences imputed to original sin. Pelagianism views the role of Jesus as "setting a good example" for the rest of humanity (thus counteracting Adam's bad example) as well as providing an atonement for our sins. In short, humanity has full control, and thus full responsibility, for obeying the Gospel in addition to full responsibility for every sin (the latter insisted upon by both proponents and opponents of Pelagianism). According to Pelagian doctrine, because humans are sinners by choice, they are therefore criminals who need the atonement of Jesus Christ. Sinners are not victims; they are criminals who need pardon.
2. Arianism was a Christian heresy first proposed early in the 4th century by the Alexandrian presbyter Arius. It affirmed that Christ is not truly divine but a created being. The fundamental premise of Arius was the uniqueness of God, who is alone self-existent and immutable. The Son, who is not self-existent, cannot be God.
3. Donatism was a Christian sect within the Roman province of Africa that flourished in the fourth and fifth centuries. It had its roots in the social pressures among the long-established Christian community of Roman North Africa (present-day) Algeria and Tunisia, during the persecutions of Christians under Diocletian. The Donatists (named for the Berber Christian bishop Donatus Magnus) were members of a schismatic church not in communion with the churches of the Catholic tradition in Late Antiquity.