In this curricular unit several aspects of Harmonic Analysis, on a beginning postgraduate level, are considered, and results and proofs are discussed on pointwise, uniform, and mean square convergence of Fourier series, as well as the summation methods of Abel and Cesàro. The discrete Fourier and Haar transforms (including FFT and FHT) are studied, as well as the Fourier transform in S and S'. The curricular unit concludes with an introductory study to Wavelet Analysis and its applications. The goal of this learning trajectory is to introduce the student to modern methods of Applied Harmonic Analysis in a relatively straightforward way, and to provide him/her with the conceptual and technical instruments that will allow him/her to understand the recent scientific literature and to proceed more advanced post-graduate studies in Applied Analysis or in other scientific and technological areas that need those instruments.