his work for advanced students and researchers explains methods for solving, within the framework of a common approach, traditional problems of approximation theory for large collections of functions, including the well-known Weyl-Nagy and Sobolev classes as particular cases, as well as classes of functions defined by convolutions with arbitrary summable kernels. Chapters cover areas including regularity of linear methods of summation of Fourier series, saturation of linear methods, classes of periodic functions, best approximations in the spaces C and L, interpolation, and approximation of Cauchy- type integrals