Intellectual Reason Is an Act of Faith
Anselm frequently wrote on faith and reason, preferring logic as the correct manner by which man should know God. This was controversial in his day, which was mostly mystic in its approach to theology. For Anselm, scholarly thought was a religious act. But, he also wrote in the Proslogion that even an atheist should be able to follow the logic toward the existence of God without religious faith as a prerequisite, given that the atheist were intelligent and honest.
Jesus's Crucifixion Was Satisfactory
Another common theme in Anselm's works concerns the nature of Jesus's sacrificial death. Anselm argues that just as the Jewish practice of animal sacrifice paid the price of their sin temporarily, Jesus's sacrifice paid the price of sin permanently.
The contemporary name for this belief is Penal Substitutionary Atonement, and although the idea is highly debated in the Christian academic community, the Anselmian model has been the dominant view of the church of almost a thousand years.
Man Can Understand Morality Through Logic
Anselm's approach to the question of moral goodness is not belief-first, logic-second. He argues that a man's subjective perception of moral goodness is only an indication in high systems of moral goodness, and that an intelligent man should be able to understand that his view is limited, and therefore, logic is the avenue for man to understand morality more correctly.