Table of contents : Title page......Page 1 Preface......Page 4 Notations......Page 6 I. Generalities......Page 7 II. Fourier series in Hilbert space......Page 21 III. Further properties of trigonometrical Fourier series......Page 28 IV. Convergence of Fourier series......Page 43 V. Summability of Fourier series......Page 59 VI. Applications of the theorems of Chapter V......Page 75 VII. General trigonometrical series......Page 89 Notes......Page 99