This book develops the mathematical theory of linear adaptive filters with finite impulse response. Examples and computer experiment applications illustrate the theory and principles. The second edition has also been restructured with an introduction followed by four parts: discrete-time wide-sense station stochastic process; linear optimum filtering; linear FIR adaptive filtering; limitations, extensions and discussions. New features includes new chapters on QR decomposition-based lattice filters, on blind deconvolution, new appendix material on complex variables and regulation.