Synopsis This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing. The necessary background in matrices, multivariate normal distribution and distributions of quadratic forms is developed along the way. It is primarily aimed at advanced undergraduate and first year masters students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. It should also be of use to research workers as a source of several standard results and problems. The development of matrix theory in the first two chapters is somewhat different from that in most texts. The concepts of rank and generalized inverse are prominently exploited. The first three chapters present the core of linear models and can form a basis for a one semester course. The last three chapters are devoted to certain special topics such as singular values, optimality in block designs and rank additivity. A rich collection of exercises is included. This is a thoroughly revised and enlarged version of the first edition. Besides correcting minor errors, new sections and problems have been added.