The theory of generalized multivariate analysis, based on elliptically contoured distributions, represents a brilliant achievement in the field of multivariate analysis. This is the first book on the subject. The text discusses estimation of parameters, testing of hypotheses, and linear models employing the method of stochastic representation, rather than following the classical treatments. It is designed as a textbook for a one-semester course at postgraduate level and as a reference source for lecturers and researchers.