Starting with the basic linear model where the design and covariance matrices are of full rank, this book demonstrates how the same statistical ideas can be used to explore the more general linear model with rank-deficient design and/or covariance matrices. The unified treatment presented here provides a clearer understanding of the General linear model from a statistical perspective, thus avoiding the complex matrix-algebraic arguments that are often used in the rank-deficient case. Elegant geometric arguments are used as needed. The book has very broad coverage, from illustrative practical examples in regression and analysis of variance alongside their implementation using R, to providing a comprehensive theory of the General linear model with 181 worked-out examples, 227 exercises with solutions, 152 exercises without solutions (so that they may be used as assignments in a course), and 320 up-to-date references. This completely updated and new edition of linear models: an integrated approach includes features such as applications with data sets, and their implementation in R, comprehensive coverage of regression diagnostics and Model building, coverage of other special topics such as collinearity, stochastic and inequality constraints, misspecified models, etc.