Classification of Integral Equations, various examples, Abel’s problem,2 nd order ordinary differential equations and Integral Equations, Initialand boundary value problems, singular boundary value problems.Integral Equations of second kind: degenerate kernels, Neumann series.Compact self-adjoint operators: Structure theorem, spectrum,Applications to integral equations, positive operators and Integralequations arising from Sturm-Liouville theory.Approximate methods for eigenvalues and eigenvecto