What does the Quran say about Women's creation and purpose?

From a tiny drop that becomes an embryo, the girl-child is born to be an honored part of God's plan. God states in the Muslim holy book, the Qur'an: "O humankind! Be conscious of your Lord Who created you from a single soul, and out of it created its mate, and out of the two spread countless men and women. Be conscious of your Lord through Whom you demand your mutual rights and honor the wombs; God always watches over you." (Qur'an 4:1) According to the Qur'an, there was a Garden of Eden. There was a forbidden tree, but no apple, no snake, and certainly no fault on Eve alone. Both Adam and Eve sinned at the same time. They felt shame, repented, and were forgiven together. God provided them with guidance, showing them a way back to Him. "Each soul earns on its own account: and no bearer of burden shall bear the burden of another." (Qur'an 6:164) "If any do deeds of righteousness, whether male or female, and have faith, they will enter Paradise and not the least injustice will be done to them." (Qur'an 4:124) The sole purpose and existence of both men and women is to worship God through faith and good deeds, fulfilling their role as God's honorable trustees and witnesses on this earth.