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Best Linear Unbiased Prediction (BLUP) has become the most widely accepted method for genetic evaluation of domestic livestock. Since its introduction, the method has evolved and despite this there is no simple text on the application of linear models to the prediction of breeding values. This book has been written with a good balance of theory and application to fill this gap. Equations for partitioning breeding values into contributions from various sources of information are derived under the various models. Recent developments in the analysis of longitudinal data with random regression models and the inclusion of genetic marker information in the evaluation of animals have been incorporated.