Find the direct statement in which Edwards sets forth the purpose of his sermon, "Sinners in the Hands of an Angry God."
Edwards laid the foundation for his sermon by establishing the background circumstances, the historic sinfulness of the ancient Israelites and the "punishment and destruction" that they brought down upon themselves. He went on to vividly and graphically describe the wrath of God and the complete justification that God had for bringing down that wrath upon humanity.
In the "Application" section of his sermon, Edwards addresses his purpose in the sermon by relating all this background information to the congregation he was addressing.
The use of this awful subject may be for awakening unconverted persons in this congregation. This that you have heard is the case of every one of you that are out of Christ. -- That world of misery, that lake of burning brimstone, is extended abroad under you.
The remainder of the sermon emphasizes and reemphasizes the urgency of the situation, the dire straits in which the congregants were currently existing and the enormity of the consequences that would inescapably fall upon them if they did not repent and change their ways. The purpose of the sermon was to bring those listening to the sermon to their knees in repentence so as to save themselves from their "Angry God."