We will present the second part of the book “Mathematical Foundations of Data Sciences” by Gabriel Peyre. The book provides an overview of important mathematical and numerical foundations for modern data sciences. It covers in particulars the basics of signal and image processing (Fourier, Wavelets, and their applications to denoising and compression), imaging sciences (inverse problems, sparsity, compressed sensing) and machine learning (linear regression, logistic classification, deep learning). The focus is on the mathematically-sounded exposition of the methodological tools (in particular linear operators, nonlinear approximation, convex optimization, optimal transport) and how they can be mapped to efficient computational algorithms. Students should seek the course instructor’s approval to take this course.