The preface of the book "Scientific Computation" provides a comprehensive overview of the evolution and current state of spectral methods in scientific computing, particularly in fluid dynamics. The authors, Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, and Thomas A. Zang, highlight the historical development of spectral methods, from their initial proposal in 1944 to their modern applications in the 21st century. They discuss the key milestones, such as the resurgence of spectral methods in the 1960s and 1970s, the development of mathematical foundations in the 1970s, and the broader application to various problems in the 1980s and 1990s. The preface also emphasizes the recent advancements in multidomain spectral methods, which have allowed for the application of spectral methods to arbitrary geometries. These methods have become increasingly important due to their high-order accuracy and ability to handle complex geometries. The authors note that while classical spectral methods remain essential, multidomain spectral methods have evolved to address new challenges, such as discontinuous problems and iterative methods for implicit equations. The book is divided into two parts: the first part focuses on the general aspects of classical spectral methods, including polynomial approximation, basic approaches to constructing spectral methods, and solution techniques for algebraic systems. The second part delves into applications in fluid dynamics and multidomain spectral methods, covering topics such as spectral algorithms for stability analysis, incompressible and compressible flow algorithms, and spectral approximations in complex domains. The preface concludes with a discussion of the practical aspects of implementing spectral methods, including numerical examples, software availability, and the authors' contributions to the field. The book aims to provide a modern and comprehensive discussion of spectral methods, reflecting the latest advancements and applications in scientific computation.The preface of the book "Scientific Computation" provides a comprehensive overview of the evolution and current state of spectral methods in scientific computing, particularly in fluid dynamics. The authors, Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, and Thomas A. Zang, highlight the historical development of spectral methods, from their initial proposal in 1944 to their modern applications in the 21st century. They discuss the key milestones, such as the resurgence of spectral methods in the 1960s and 1970s, the development of mathematical foundations in the 1970s, and the broader application to various problems in the 1980s and 1990s. The preface also emphasizes the recent advancements in multidomain spectral methods, which have allowed for the application of spectral methods to arbitrary geometries. These methods have become increasingly important due to their high-order accuracy and ability to handle complex geometries. The authors note that while classical spectral methods remain essential, multidomain spectral methods have evolved to address new challenges, such as discontinuous problems and iterative methods for implicit equations. The book is divided into two parts: the first part focuses on the general aspects of classical spectral methods, including polynomial approximation, basic approaches to constructing spectral methods, and solution techniques for algebraic systems. The second part delves into applications in fluid dynamics and multidomain spectral methods, covering topics such as spectral algorithms for stability analysis, incompressible and compressible flow algorithms, and spectral approximations in complex domains. The preface concludes with a discussion of the practical aspects of implementing spectral methods, including numerical examples, software availability, and the authors' contributions to the field. The book aims to provide a modern and comprehensive discussion of spectral methods, reflecting the latest advancements and applications in scientific computation.