There are many important ideas put forth by The Gay Science, but the book seems to be a compendium of various ideas and conclusions. It includes songs.
In the beginning, Nietzsche discusses the way all life seems related to power. He discusses various types of power, including social and economic power, but also the autonomy of free choice. He mentions the theme of recurrence, arguing that perhaps we are all locked in an infinite cycle of reincarnations into the same lives, over and over again, forever. These nightmarish meditations continue until Nietzsche reaches his most famous conclusion for the first time in his published writings.
The famous line is, "God is dead." He discusses the way Buddhism survived as a religion, and he states God's death and points observes the fact that God will still be followed for millenniums yet. He urges his reader to abandon their attachment to divinity.
The Gay Science concludes with one of the most famous vignettes from Nietzsche's early writings. The parable of the madman (as the passage has been called) is about an insane man who walks into a town holding a candle, though it's midday on a sunny day. The townsmen gather, and the madman declares that we ourselves have killed God. They ask him about his candle and he claims that without God, no man should trust what they see by the light of the sun, because God made that sun. If there is no God, there certainly is no sun.
