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The article reviews the statistical theory of signal detection in applicationto analysis of deterministic gravitational-wave signals in the noise of adetector. Statistical foundations for the theory of signal detection andparameter estimation are presented. Several tools needed for both theoreticalevaluation of the optimal data analysis methods and for their practicalimplementation are introduced. They include optimal signal-to-noise ratio,Fisher matrix, false alarm and detection probabilities, $\F$-statistic,template placement, and fitting factor. These tools apply to the case ofsignals buried in a stationary and Gaussian noise. Algorithms to efficientlyimplement the optimal data analysis techniques are discussed. Formulas aregiven for a general gravitational-wave signal that includes as special casesmost of the deterministic signals of interest.

Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case