Book excerpt: Based on the author’s own research, this book rigorously and systematically develops the theory of Gaussian white noise measures on Hilbert spaces to provide a comprehensive account of nonlinear filtering theory. Covers Markov processes, cylinder and quasi-cylinder probabilities and conditional expectation as well as predictio0n and smoothing and the varied processes used in filtering. Especially useful for electronic engineers and mathematical statisticians for explaining the systematic use of finely additive white noise theory leading to a more simplified and direct presentation.