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Introduction. 1. Background information. 2. Noetherity criterion and a formula for the index of a singular integral functional operator of first order in the continuous case. 3. The Noether theory of a singular integral functional operator of finite order in the continuous case. 4. The Noether theory of singular integral functional operators with continuous coefficients on a non-closed contour. 5. The Noether theory in algebras of singular integral functional operators. References. Index.