2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96663Carleson's Theorem asserts the pointwise convergence of Fourier series of square integrable functions. We give a complete proof, following joint work of the author and C. Thiele. Over 20 exercises are also detailed. We also discuss the derviation of the theorem on L^p spaces. And discuss a number of complements and extensions of the theorem and proof of Carleson's theorem.An expanded version of the published article (Publ. Mat. (2004) no.2 251-307.) With additional material, updated references, and over 100 references in totalClassical Analysis and ODEs42text