Fundamental to any livestock improvement programme by animal scientists, is the prediction of genetic merit in the offspring generation for desirable production traits such as increased growth rate, or superior meat, milk and wool production. Covering the foundational principles on the application of linear models for the prediction of genetic merit in livestock, this new edition is fully updated to incorporate recent advances in genomic prediction approaches, genomic models for multi-breed and crossbred performance, dominance and epistasis. It provides models for the analysis of main production traits as well as functional traits and includes numerous worked examples. For the first time, R codes for key examples in the textbook are provided online. The book covers: - The relationship between the genome and the phenotype. - BLUP models for various livestock data and structure. - Incorporation of related ancestral parents and metafounders in prediction models. - Models for survival analysis and social interaction. - Advancements in genomic prediction approaches and selection. - Genomic models for multi-breed and crossbred performance. - Models for non-additive genetic effects including dominance and epistasis. - Estimation of genetic parameters including Gibbs sampling approaches. - Computation methods for solving linear mixed model equations. Suitable for graduate and postgraduate students, researchers and lecturers of animal breeding, genetics and genomics, this established textbook provides a thorough grounding in both the basics and in new developments of linear models and animal genetics.