This book gives a comprehensive overview of both the 　　fundamentals of wavelet analysis and related tools, and of the 　　most active recent developments towards applications. It offers a 　　state of the art in several active areas of research where 　　wavelet ideas, or more generally multiresolution ideas have 　　proved particularly effective. 　　 The main applications covered are in the numerical analysis 　　of PDEs, and signal and image processing. Recently introduced 　　techniques such as Empirical Mode Decomposition (EMD) and new 　　trends in the recovery of missing data, such as compressed 　　sensing, are also presented. Applications range for the 　　reconstruction of noisy or blurred images, pattern and face 　　recognition, to nonlinear approximation in strongly anisotropic 　　contexts, and to the classification tools based on multifractal 　　analysis.