Preface. Introduction. 1. Classes of periodic functions. 2. Integral representations of deviations of linear means of Fourier series. 3. Approximations by Fourier sums in the spaces c and L1. 4. Simultaneous approximation of functions and their derivatives by Fourier sums. 5. Convergence rate of Fourier series and best approximations in the spaces Lp. 6. Best approximations in the spaces C and L. Bibliographical notes. References. Index.