What are the sins that anger Allah Almighty, and what are the greatest unforgivable sins?

God's wrath upon a servant comes about by committing forbidden acts or by neglecting obligatory duties. This wrath is commensurate with the severity of the sins and the importance of the duties. Among the matters for which the Quran explicitly states God's wrath upon the doer is the unlawful taking of a life. The greatest sin in the sight of God is polytheism (shirk), and it is the only sin that is not forgiven except through repentance. Allah says: "Indeed, Allah does not forgive association with Him, but He forgives what is less than that for whom He wills. And whoever associates others with Allah has certainly fabricated a tremendous sin."