Volume 1 Introductory material Chapter I: Basic concepts and theorems in the theory of trigonometric series Chapter II: Fourier coefficients Chapter III: The convergence of a Fourier series at a point Chapter IV: Fourier series of continuous functions Chapter V: Convergence and divergence of a Fourier series in a set Chapter VI: "Adjustment" of functions in a set of small measure Appendix Bibliography Volume 2 Chapter VII: The summability of Fourier series. Additional investigation into problems of convergence Chapter VIII: Conjugate trigonometric series Chapter IX: Absolute convergence of Fourier series Chapter X: Sine and cosine series with monotonically decreasing coefficients Chapter XI: Lacunary series Chapter XII: Convergence and divergence of general trigonometric series Chapter XIII: The absolute convergence of general trigonometric series Chapter XIV: Problems of uniqueness of the expansion of a function into a trigonometric series Chapter XV: Representation of a function by a trigonometric series Appendix Bibliography