Pope begins the essay addressing his friend, St. John, and proposes the overall object which is to "vindicate the ways of God to man." This means that the general object of man's study should be to explain the world as God has planned it. Man (humans) should seek to understand the goodness of the universe and how we fit into it. Our purpose is to understand this by seeking to find individual, social, and spiritual harmony. This is the general outline. 

Man (humankind) should not be so proud or arrogant as to attempt to know the mind of God. Man should focus on his own nature: 

Know then thyself, presume not God to scan;

The proper study of mankind is Man. (Epistle 2.1-2) 

Since all of creation is created in a continuous, harmonious whole, man should strive to understand his part in nature. In understanding his part, man might begin to understand the whole. 

And although there is evil in the world, man shouldn't think that God made an imperfect world. Rather, evil in the world is a necessary part of man's place in the universe. One way to fit this into the grand scheme of the harmonious universe is that with the presence of evil, man has choice and that choice might be used to make a better future. 

Pope explains that the universe is governed by reason. And although we might not understand everything, there there is a cosmic unity to everything. 

And, spite of pride, in erring reason's spite, 

One truth is clear: Whatever IS, is RIGHT. (Epistle 1.293-4)