The course is an introduction to the Fourier Analysis for graduate students in Mathematics. The syllabus includes Fourier series (point wise and uniform convergence, Riemann localization Principle, norm convergence, summability, examples of divergent Fourier series); Fourier Transform (basic properties, Riemann -Lebesgue lemma, inversion, L2-theory in Rn); Fourier Analysis in Lp-spaces (Riesz-Thorin interpolation theorem, Hilbert transform).