In this book, Paul asks Philemon to forgive his runaway slave Onesimus. This is a revolutionary act, demonstrating the Gospel in action and showing that all people are equal partners in the new humanity.
Paul urges Philemon to forgive Onesimus and accept him back as an equal. Because they are both believers, God's grace and healing mercy have made them partners under the new humanity Jesus' established.
While Paul doesn't mention Jesus' death and resurrection directly in this book, he offers to take on any punishment Onesimus deserves, a demonstration of what Jesus did on the cross. He encourages Philemon to do the same as he reconciles to Onesimus before God.