C.S. Lewis
The author of The Problem of Pain, C.S. Lewis was a Christian academic, theologian, essayist, and fiction writer who is considered one of history's greatest apologists. In this book, his views and intentions are obvious: he wants to address a common objection to the Christian faith and evaluate its tenability. In the course of this work, Lewis presents a partial theodicy, proving that the issue of suffering in the world is not sufficient reason to disbelieve in God.
God
In Christian tradition, God is seen as the Creator of the universe and of mankind. He is the target of the argument to which Lewis responds, which holds that since there is suffering in the world, God cannot be both all-good (making him want to stop it) and all-powerful (making him able to stop it). Lewis defends God from this attack on his character; God is ultimately powerful and knowledgeable, and who are we to question his methods? Instead of relying solely on this unsatisfactory answer, Lewis puts forward good reasons to believe that if God were all-good and all-powerful, our reality would look exactly the same as it does now.
Christ
According to Christian Scripture, Jesus Christ is the Son of God, fully God and fully man, who descended to Earth and died to take on the burden of humanity's sins before resurrecting and ascending back into Heaven. Although Christ doesn't figure as prominently as God in this discussion, he is nevertheless present, as his salvific work is crucial for understanding God's nature and the Christian narrative as a whole.
Adam
In Christian tradition, Adam was the first man God created in the beginning, just before the creation of Eve, Adam's wife. Although Adam and Eve "walked with God" in the Garden of Eden, they chose to rebel and sin against God, severing the perfect relationship between Creator and creature. Adam is often used as a representation of original sin, as well as a metonymic figure to explain the fall of man. In The Problem of Pain, Lewis references Adam's fall as a reason why the current world is so broken, a result of sin entering the world.
Satan
The last primary figure in The Problem of Pain is Satan, otherwise known as the Devil. Once an angel named Lucifer, Satan led a rebellion against God in Heaven and was cast out, along with all of his followers. It is also commonly accepted that he appeared to Eve in the Garden of Eden in the form of a snake, tempting her to sin. Satan's role in this book is limited, but his influence is important; Lewis argues that Lucifer's rebellion occurred before that of Adam and Eve, making the world already fallen before the humans sinned as well.