This course is an introduction to Fourier series and Fourier transform. Topics include: Orthogonal families of functions, mean-square convergence of Fourier series and completeness, pointwise convergence of Fourier series, Gibbs’s phenomenon; Fourier transform and its inversion, Plancherel formula. Further topics will be selected from: The isoperimetric inequality, Poisson summation formula Heisenberg uncertainty principle, and the notion of a wavelet.