General ideas of the recursion operator method and adjoint representation -- Linear matrix bundle -- BC group and general integrable equations under reductions -- Quadratic bundle with Z 2 grading -- Polynomial and rational bundles -- Polynomial and rational bundles -- General differential spectral problem -- Generalization and reductions of the differential spectral problem and integrodifferential spectral problems -- Two-dimensional matrix spectral problem -- Two-dimensional differential spectral problem -- Towards to the general theory of recursion structure of nonlinear evolution equations.