This book contains a number of problems with signal detection theory. A generalized observation model for signal detection problems, is presented. The model includes several interesting and common special cases such as those describing additive noise, multiplicative noise, and signal-dependent noise. This model can also describe composite signals in addition to the usual known (deterministic) signals and random (stochastic) signals. Locally optimum (LO) and locally optimum rank (LOR) detectors for known and random signals in the model, are discussed, and original results are obtained. Other approaches to detection of signals also are discussed.