1 Reference Material -- 1.1 Introduction -- 1.2 Singular Integral Equations -- 1.3 Improper Integrals -- 1.4 The Lebesgue Integral -- 1.5 Cauchy Principal Value for Integrals -- 1.6 The Hadamard Finite Part -- 1.7 Spaces of Functions and Distributions -- 1.8 Integral Transform Methods -- 1.9 Bibliographical Notes -- 2 Abel's and Related Integral Equations -- 2.1 Introduction -- 2.2 Abel's Equation -- 2.3 Related Integral Equations -- 2.4 The equation $$\int_{0}^{s} {{{{(s - t)}}^{\beta }}g(t)dt = f(s), \Re e \beta > - 1}$$ -- 2.5 Path of Integration in the Complex Plane -- 2.6 The Equation $$\int_{{{{C}_{{a\xi }}}}} {\frac{{g(z)dz}}{{{{{(z - \xi )}}^{\nu }}}}} + k\int_{{{{C}_{{\xi b}}}}} {\frac{{g(z)dz}}{{{{{(\xi - z)}}^{\nu }}}}} = f(\xi )$$ -- 2.7 Equations on a Closed Curve -- 2.8 Examples -- 2.9 Bibliographical Notes -- 2.10 Problems -- 3 Cauchy Type Integral Equations -- 3.1 Introduction -- 3.2 Cauchy Type Equation of the First Kind -- 3.3 An Alternative Approach -- 3.4 Cauchy Type Equations of the Second Kind -- 3.5 Cauchy Type Equations on a Closed Contour -- 3.6 Analytic Representation of Functions -- 3.7 Sectionally Analytic Functions (z?a)n?v(z?b)m+v -- 3.8 Cauchy's Integral Equation on an Open Contour -- 3.9 Disjoint Contours -- 3.10 Contours That Extend to Infinity -- 3.11 The Hilbert Kernel -- 3.12 The Hilbert Equation -- 3.13 Bibliographical Notes -- 3.14 Problems -- 4 Carleman Type Integral Equations -- 4.1 Introduction -- 4.2 Carleman Type Equation over a Real Interval -- 4.3 The Riemann-Hilbert Problem -- 4.4 Carleman Type Equations on a Closed Contour -- 4.5 Non-Normal Problems -- 4.6 A Factorization Procedure -- 4.7 An Operational Approach -- 4.8 Solution of a Related Integral Equation -- 4.9 Bibliographical Notes -- 4.10 Problems -- 5 Distributional Solutions of Singular Integral Equations -- 5.1 Introduction -- 5.2 Spaces of Generalized Functions -- 5.3 Generalized Solution of the Abel Equation -- 5.4 Integral Equations Related to Abel's Equation -- 5.5 The Fractional Integration Operators ?? -- 5.6 The Cauchy Integral Equation over a Finite Interval -- 5.7 Analytic Representation of Distributions of ?'[a, b] -- 5.8 Boundary Problems in A[a,b] -- 5.9 Disjoint Intervals -- 5.10 Equations Involving Periodic Distributions -- 5.11 Bibliographical Notes -- 5.12 Problems -- 6 Distributional Equations on the Whole Line -- 6.1 Introduction -- 6.2 Preliminaries -- 6.3 The Hilbert Transform of Distributions -- 6.4 Analytic Representation -- 6.5 Asymptotic Estimates -- 6.6 Distributional Solutions of Integral Equations -- 6.7 Non-Normal Equations -- 6.8 Bibliographical Notes -- 6.9 Problems -- 7 Integral Equations with Logarithmic Kernels -- 7.1 Introduction -- 7.2 Expansion of the Kernel In /x-y/ -- 7.3 The Equation $$\int_{a}^{b} {\ln } \left/ {x - y} \right/g(y)dy = f(x)$$ -- 7.4 Two Related Operators -- 7.5 Generalized Solutions of Equations with Logarithmic Kernels -- 7.6 The Operator $$\int_{a}^{b} {(P(x - y)\ln \left/ {x - y} \right/ + Q(x,y))g(y)dy}$$ -- 7.7 Disjoint Intervals of Integration -- 7.8 An Equation Over a Semi-Infinite Interval -- 7.9 The Equation of the Second Kind Over a Semi-Infinite Interval -- 7.10 Asymptotic Behavior of Eigenvalues -- 7.11 Bibliographical Notes -- 7.12 Problems -- 8 Wiener-Hopf Integral Equations -- 8.1 Introduction -- 8.2 The Holomorphic Fourier Transform -- 8.3 The Mathematical Technique -- 8.4 The Distributional Wiener-Hopf Operators -- 8.5 Illustrations -- 8.6 Bibliographical Notes -- 8.7 Problems -- 9 Dual and Triple Integral Equations -- 9.1 Introduction -- 9.2 The Hankel Transform -- 9.3 Dual Equations with Trigonometric Kernels -- 9.4 Beltrami's Dual Integral Equations -- 9.5 Some Triple Integral Equations -- 9.6 Erdélyi-Köber Operators -- 9.7 Dual Integral Equations of the Titchmarsh Type -- 9.8 Distributional Solutions of Dual Integral Equations -- 9.9 Bibliographical Notes -- 9.10 Problems -- References.