This textbook introduces sparse and redundant representations with a focus on applications in signal and image processing. The theoretical and numerical foundations are tackled before the applications are discussed. Mathematical modeling for signal sources is discussed along with how to use the proper model for tasks such as denoising, restoration, separation, interpolation and extrapolation, compression, sampling, analysis and synthesis, detection, recognition, and more. The presentation is elegant and engaging. Sparse and Red undant Representations is intended for graduate students in applied mathematics and electrical engineering, as well as applied mathematicians, engineers, and researchers who are active in the fields of signal and image processing.