On the works of S. B. Stechkin on approximation of periodic functions by polynomials

We give a survey of S. B. Stechkin's works devoted to the following themes: direct and inverse theorems in the theory of best approximations; finding the order of decreasing of Kolmogorov's width for classes of differentiable functions; approximative properties of partial sums of Fourier and Taylor series as well as that of the Fejèr and Valleé Poussin sums; the criterion of absolute convergence for Fourier series in terms of $n$-term approximation.