1 On Fredholmness of Singular Type Operators. - 1 Fredholm operators. - 2 Singular integral operators with piecewise continuous coefficients in the space Lp(?). - 3 On Fredholmness of convolution type operators. - 4 Bibliographic notes to Chapter 1. - 2 On Fredholmness of Other Singular-type Operators. - 5 On operators with homogeneous kernels; the one-dimensional case. - 6 Operators with homogeneous kernels; the multi-dimensional case. - 7 Convolution-type operators with discontinuous symbols. - 8 Bibliographic notes to Chapter 2. - 3 Functional and Singular Integral Equations with Carleman Shifts in the Case of Continuous Coefficients. - 9 Carleman and generalized Carleman shifts1ll. - 10 A functional equation with shift. - 11 Singular integral equations with Carleman shift on a closed curve; the case of continuous coefficients. - 12 Singular integral equations with Carleman shift on an open curve; the case of continuous coefficients. - 13 Bibliographic notes to Chapter 3. - 4 Two-term Equations (A + QB)? = f with an Involutive Operator Q; an Abstract Approach and Applications. - 14 Fredholmness of an abstract equation with an involutive operator; non-matrix approach. - 15 Application to singular integral equations with complex conjugate unknowns. - 16 Applications to integral equations on the real line with reflection or inversion. - 17 Application to singular integral equations with Carleman shift on an open curve; the case of discontinuous coefficients. - 18 Singular integral equations with a fractional linear shift in the space Lp with a special weight. - 19 Fredholmness of abstract equations with a generalized involutive operator (non-matrix approach). - 20 Abstract equations with algebraic operators. - 21 Bibliographic notes to Chapter 4. - 5 Equations with Several GeneralizedInvolutive Operators. Matrix Abstract Approach and Applications. - 22 Fredholmness of abstract equations with generalized involutive operators (matrix approach). - 23 Singular integral equations with a finite group of shifts in the case of continuous coefficients. - 24 Singular integral equations with a finite group of shifts (the case of piecewise continuous coefficients). - 25 Convolution type equations with shifts and complex conjugation. - 26 Bibliographic notes to Chapter 5. - 6 Application of the Abstract Approach to Singular Equation on the Real Line with Fractional Linear Shift. - 27 Singular integral operators perturbed by integral operators with homogeneous kernels. - 28 Singular integral operators with a fractional linear Carleman shift in the weighted space Lp?(Rl). - 29 Equations including operators with homogeneous kernels the singular integral operators and the inversion shift. - 30. Potential type operators on the real 1ine with a fractional linear Carleman shift. - 31 Generalized Carleman fractional linear shifts on the real line. - 32 Singular integral equations with a generalized Carleman fractional linear shift. - 33. Bibliographic Notes to Chapter 6. - 7 Application to Hankel Type and Multidimensional Integral Equations. - 34 Convolution integral equations of Hankel type. - 35 Some multidimensional singular type equations with shifts. - 36 Bibliographic Notes to Chapter 7. - List of Symbols. Language: English