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This book contains a unified treatment of a class of problems of signal detection theory. This is the detection of signals in addi- tive noise which is not required to have Gaussian probability den- sity functions in its statistical description. For the most part the material developed here can be classified as belonging to the gen- eral body of results of parametric theory. Thus the probability density functions of the observations are assumed to be known, at least to within a finite number of unknown parameters in a known functional form. Of course the focus is on noise which is not Gaussian; results for Gaussian noise in the problems treated here become special cases. The contents also form a bridge between the classical results of signal detection in Gaussian noise and those of nonparametric and robust signal detection, which are not con- sidered in this book. Three canonical problems of signal detection in additive noise are covered here. These allow between them formulation of a range of specific detection problems arising in applications such as radar and sonar, binary signaling, and pattern recognition and classification. The simplest to state and perhaps the most widely studied of all is the problem of detecting a completely known deterministic signal in noise. Also considered here is the detection random non-deterministic signal in noise. Both of these situa- of a tions may arise for observation processes of the low-pass type and also for processes of the band-pass type.