Wavelets have become part of the toolbox of scientist. Wherever a signal or image needs to be analyzed, the wavelet transform can be used. Wavelets provide a "mathematical zoom" that permits one to analyze functions and operators at many scales simultaneously. Wavelets have wonderful approximation properties. From the mathematical point of view they provide bases for a number of classical spaces of functions. From the practical point of view they permit to represent certain signals very efficiently. Wavelets are being used to study turbulence and PDE's. They also have become a popular denoising tool. In this course, Dr. Pereyra will explain: (a) the basics of wavelets and signal/image compression; (b) how to construct divergence-free multi-wavelets which are expected to be useful in numerical analysis of incompressible fluids; (c) denoising procedures and compare wavelet techniques to classical denoising techniques; and (d) what wavelets are, how to construct them, and how to implement them.