Press Book. The Macmillan Co., New York 1964. Antoni Zygmund, Trigonometric series, Vol. I, II. Third edition. With a foreword by Robert A. Fefferman. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2002. Yitzhak Katznelson, An introduction to harmonic analysis, Third edition. Cambridge University Press, Cambridge, 2004. Karl R. Stromberg, Introduction to classical analysis, Wadsworth International Group, 1981. The Katznelson book is the one using the most modern terminology and style of the three. The original publishing dates are: Zygmund in 1935, Bari in 1961 and Katznelson in 1968. Zygmund's book was greatly expanded in its second publishing in 1959, however. Articles referred to in the text Paul du Bois-Reymond, "Ueber die Fourierschen Reihen", Nachr. Kön. Ges. Wiss. Göttingen 21 (1873), 571–582. This is the first proof that the Fourier series of a continuous function might diverge. In German Andrey Kolmogorov, "Une série de Fourier–Lebesgue divergente presque partout", Fundamenta Mathematicae 4 (1923), 324–328. Andrey Kolmogorov, "Une série de Fourier–Lebesgue divergente partout", C. R. Acad. Sci. Paris 183 (1926), 1327–1328 The first is a construction of an integrable function whose Fourier series diverges almost everywhere. The second is a strengthening to divergence everywhere. In French. Lennart Carleson, "On convergence and growth of partial sums of Fourier series", Acta Math. 116 (1966) 135–157. Richard A. Hunt, "On the convergence of Fourier series", Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967), 235–255. Southern Illinois Univ. Press, Carbondale, Ill. Charles Louis Fefferman, "Pointwise convergence of Fourier series", Ann. of Math. 98 (1973), 551–571. Michael Lacey and Christoph Thiele, "A proof of boundedness of the Carleson operator", Math. Res. Lett. 7:4 (2000), 361–370. Ole G. Jørsboe and Leif Mejlbro, The Carleson–Hunt theorem on Fourier series. Lecture Notes in Mathematics 911, Springer-Verlag, Berlin-New York, 1982. This is the original paper of Carleson, where he proves that the Fourier expansion of any continuous function converges almost everywhere; the paper of Hunt where he generalizes it to spaces; two attempts at simplifying the proof; and a book that gives a self contained exposition of it. Dunham Jackson, Fourier Series and Orthogonal Polynomials, 1963 D. J. Newman, "A simple proof of Wiener's 1/f theorem", Proc. Amer. Math. Soc. 48 (1975), 264–265. Jean-Pierre Kahane and Yitzhak Katznelson, "Sur les ensembles de divergence des séries trigonométriques", Studia Math. 26 (1966), 305–306 In this paper the authors show that for any set of zero measure there exists a continuous function