Thisbookpresentsmaterialwhichismorealgorithmicallyorientedthanmost alternatives.Italsodealswithtopicsthatareatorbeyondthestateoftheart. Examples include practical and applicable wavelet and other multiresolution transform analysis. New areas are broached like the ridgelet and curvelet transforms. The reader will ?nd in this book an engineering approach to the interpretation of scienti?c data. Compared to the 1st Edition, various additions have been made throu- out, and the topics covered have been updated. The background or en- ronment of this book s topics include continuing interest in e-science and the virtual observatory, which are based on web based and increasingly web service based science and engineering. Additional colleagues whom we would like to acknowledge in this 2nd edition include: Bedros Afeyan, Nabila Aghanim, Emmanuel Cand` es, David Donoho, Jalal Fadili, and Sandrine Pires, We would like to particularly - knowledge Olivier Forni who contributed to the discussion on compression of hyperspectral data, Yassir Moudden on multiwavelength data analysis and Vicent Mart ?nez on the genus function. The cover image to this 2nd edition is from the Deep Impact project. It was taken approximately 8 minutes after impact on 4 July 2005 with the CLEAR6 ?lter and deconvolved using the Richardson-Lucy method. We thank Don Lindler, Ivo Busko, Mike A Hearn and the Deep Impact team for the processing of this image and for providing it to us.