This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis:Sparse Representations, Compressed Sensing and Multifractal Analysis". Newinteractions between harmonic analysis and signal and image processing haveseen striking development in the last 10 years, and several technologicaldeadlocks have been solved through the resolution of deep theoretical problemsin harmonic analysis. New Trends in Applied Harmonic Analysis focuses on twoparticularly active areas that are representative of such advances:multifractal analysis, and sparse representation and compressed sensing. Thecontributions are written by leaders in these areas, and cover boththeoretical aspects and applications. This work should prove useful not only toPhD students and postdocs in mathematics and signal and image processing,but also to researchers working in related topics.