Girard has this very original reading of myths, Greek tragedy and the Bible. It is sometimes difficult to read, especially if you're not acquainted with the work of others he refers to.
Girard argues that human beings are violent and that societies are in constant danger of falling into the downward spiral of violent revenge. To prevent this, primitive societies use sacrifices. A sacrifice is an act of violence towards an object that doesn't take revenge in return. That is why the violence stops. This is what constitutes civilisation. From this, Girard goes on to explain how this works and that in every society there is a scapegoat mechanism that seeks a scapegoat in order to reaffirm the group. The examples from mythology and tragedy are numerous and very interesting.