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Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject was still fairly novel. Motivated by the many favorable comments we have received and the continuing interest in that book (which will be referred to as CHQZ1), and yet desiring to present a more modern perspective, we embarked on the project which resulted in our recent book (Canuto et al. (2006), referred to as CHQZ2) and the present new book (referred to as CHQZ3). | C.Canuto M.Y. Hussaini A.Quarteroni -T.A.Zang Spectral Methods Evolution to Complex Geometries and Applications to Fluid Dynamics Scientific Computation Springer Scientific Computation Editorial Board J.-J. Chattot Davis CA USA P. Colella Berkeley CA USA W. E Princeton NJ USA R. Glowinski Houston TX USA M. Holt Berkeley CA USA Y. Hussaini Tallahassee FL USA P. Joly Le Chesnay France H.B. Keller Pasadena CA USA J.E. Marsden Pasadena CA USA D.I. Meiron Pasadena CA USA O. Pironneau Paris France A. Quarteroni Lausanne Switzerland and Politecnico of Milan Italy J. Rappaz Lausanne Switzerland R. Rosner Chicago IL USA P. Sagaut Paris France J.H. Seinfeld Pasadena CA USA A. Szepessy Stockholm Sweden M.F. Wheeler Austin TX USA C. Canuto M. Y. Hussaini A. Quarteroni T. A. Zang Spectral Methods Evolution to Complex Geometries and Applications to Fluid Dynamics With 183 Figures and 11 Tables 1 .