The monograph contains an exposition of the theory of trigonometric series in its present state. In particular, for the first time it contains remarkable studies by D.E. Menshov, as well as studies by a number of other modern Soviet and foreign authors. The whole theory of Fourier series is laid out on the basis of the Lebesgue integral; along with the theory of Fourier series, questions of the general theory of trigonometric series are developed in detail.