Gustaf Aulén's Christus Victor, first published in 1931, has influenced the way generations of students think about Christ's death. According to Aulén's typology, there are three main types of atonement theory: (1) the "classical" ransom theory, according to which God used Jesus as bait to rescue humanity from subjugation to the devil; (2) the "objective" satisfaction theory, according to which Jesus' death satisfies the demands of God's honour or justice; and (3) the "subjective" moral influence theory, according to which Jesus' obedient death has an exemplary moral power that can be imitated by others.
I do not believe Aulén's typology is a reliable guide to the Christian tradition. Some comments on each of his three types: (1) His first category – intended to represent patristic thought – is a real muddle. The importance it gives to the role of the devil is very misleading. The image of Jesus as bait on a hook has no frequency or importance in patristic literature, and does not represent any typical understanding of Jesus' death. Aulén has mistaken an eccentricity for a type. (2) His second category, satisfaction, is the only one that strikes me as broadly reliable. (3) His third category, moral influence, is historically so marginal that it is quite misleading to include it at all. This category might have been interesting as a characterisation of patristic thought if it had been set against the backdrop of early Christian ideas about the spiritual power of imitation. But linking this category to Abelard makes it a mere triviality, of no real importance in the tradition. Again Aulén has made a type out of an eccentricity.
I've been teaching christology this semester (using mainly patristic sources), which has got me musing about alternative typologies of Christian views of salvation. So here's a suggested typology of six themes in patristic literature:
1. Christ the Second Adam. A major theme most powerfully developed by Irenaeus in his account of recapitulation. Christ restarts the human race from the beginning and sets it on a course towards life. Christ replaces Adam as the new life-giving head of the human family. (Main scriptural source: Romans 5.)
2. Christ the Sacrifice. This is an important background theme that becomes explicit mainly in liturgical texts. Melito of Sardis' On Pascha provides the most vivid elaboration of sacrificial imagery, artfully interwoven with a plethora of other Old Testament themes and images. (Main scriptural source: the Pentateuch and the Gospel of John.)
3. Christ the Teacher. A characteristic theme of the Alexandrian tradition. Christ is the divine pedagogue who, by a slow and patient process, leads human souls up into the presence of divine wisdom. In some accounts this process extends into the afterlife. Clement of Alexandria developed this theme explicitly. The same theme supplies the basic architecture of Origen's thought. Many accounts of deification are really just elaborations of the end result of this educational process: life is a school, and deification is the graduation prize. (Main scriptural source: the four Gospels.)
4. Christ the Brother. The adoption theme is prevalent in early Christian writing. Christ becomes our brother. Through him we become members of God's family. What he is by nature, we become by grace. It is often in this context that language of deification is used: Christ is God by nature, and as his brothers and sisters we become gods by grace. Adoption language is especially pervasive in Origen. By the fourth and fifth centuries the emphasis tends to fall more on deification, but the deification theme should still be understood as a subset of either the adoption theme or the education theme (#3 above). (Main scriptural source: Romans 8.)
5. Christ the Life-giver. One finds this theme everywhere in early Christian liturgical and theological texts. It is developed with an impressive systematic rigour in the work of Athanasius. The divine Logos had to become incarnate in order to become capable of dying; by entering into death, he absorbs death into the divine life, thus draining away death's power; and by rising again, he transforms corruptible human nature into a glorious incorruptible nature. Here Christ's death and resurrection are equally emphasised as the two poles of the saving event. (Main scriptural source: 1 Corinthians 15.)
6. Christ the Healer. My impression is that this theme recurs more than any other soteriological theme in patristic writing, even though it is seldom developed in much detail. Very frequently Christ is described as a physician who cures our illness. Often he is also described as medicine. Gregory of Nazianzus speaks of the incarnation as a healing of human nature. Augustine is particularly fond of the healing theme, and it is a constant refrain in his sermons. He speaks of Adam as infecting the human race with the disease of pride, and of Christ's humility as the medicine that cures us. (Main scriptural source: the four Gospels.)
Comments: (a) Note that these themes are normally found not as separate ideas but as closely interwoven motifs. (b) Note the pronounced tendency to speak of salvation in corporate terms. Christ achieves salvation not for individuals but for human nature, for humanity as a whole. Only in the third theme (teaching) is there a more individual emphasis, but even here patristic authors believe that the whole of humanity is enrolled in Christ's school. Saints and martyrs are in the PhD program; the wicked are in kindergarten. (c) Note that only in the second category (sacrifice) is there any exclusive fixation on Christ's death as a saving event. Much more characteristic of early Christian writing is a broad vision of Christ's life, death, descent into hell, and resurrection as the one great drama of salvation. Even the sacrificial imagery that dominated early Christian interpretations of the passover (e.g. Melito's On Pascha) was qualified when Origen (in his own On Pascha) argued that the passover is not a type of Christ's sacrificial death, but a type of the whole movement whereby Christ's death, descent, and resurrection leads the human race on an exodus from death to life.