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The texts of this book grew from an ISFM A (Sino-French Institute of Applied Mathematics) symposium on "Wavelet Methods in Mathematical Analysis and Engineering" that took place in August 2007 on the Zhuhai campus of Sun Yat-Sen University. This symposium was composed of a one week summer school mainly directed towards Chinese PhD students and postdocs, followed by a one week conference attended by researchers from all over the world. This event was co-organized by Sun Yat-Sen University in Guangzhou and the ISFMA in Shangai. The purpose of the courses was to give the students the required level in wavelet analysis and in the main applications that would be treated during the conference, so that they would be able to follow it with profit. The courses were given by Albert Cohen, Daoqinq Dai, Stephane Jaffard, Lixin Shen, Zuowei Shen and Lihua Yang they covered basic materials concerning construction of properties of wavelet bases, and alternative decomposition methods they gave an overview of the main applications in the numerical analysis of PDEs, and signal and image processing. The workshop exposed new techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, and a sample of a few recent key applications of wavelets in several scientific areas. This event was part of a long term collaboration between Chinese, Singaporean and French mathematicians in the area of wavelet analysis, and a second event took place one year later, with the "Chinese-French-Singaporean Joint Workshop on Wavelet Theory and Applications" in Singapore (June 2008)