This book is intended to be an introduction to the fundamentals and methods of spectral analysis and filter theory and their appli cations in geophysics. The principles and theoretical basis of the various methods are described, their efficiency and effectiveness eval uated, and instructions provided for their practical application. Be sides the conventional methods, newer methods arediscussed, such as the spectral analysis ofrandom processes by fitting models to the ob served data, maximum-entropy spectral analysis and maximum-like lihood spectral analysis, the Wiener and Kalman filtering methods, homomorphic deconvolution, and adaptive methods for nonstation ary processes. Multidimensional spectral analysis and filtering, as well as multichannel filters, are given extensive treatment. The book provides a survey of the state-of-the-art of spectral analysis and fil ter theory. The importance and possibilities ofspectral analysis and filter theory in geophysics for data acquisition, processing and eval uation are illustrated with practical examples from various fields of applied geophysics. Although this book was planned primarily as a textbook for a course on the analysis of geophysical time· series, it may also be of interest to scientists and engineers who process other digital data. It provides a comprehensive discussion of the theoretical fundamen tals and a compilation of the extensive literature on the subject. I hope that I have succeeded in presenting the various principles and methods of time-series analysis comprehensively and without error. Comments on errors or suggestions for improvements are welcome.