Animal models have been the main statistical model for the genetic evaluation of livestock since 1989, although the theory goes back to the mid 1960's. This book covers the background, the theory, and practical applications of animal models that every serious animal breeder should understand. Examples are given in R-scripts and there is a chapter describing a Fortran program for large data sets. Matrix algebra is assumed known by the reader, as well as terminology in animal breeding. The book is a coalescence of 50 years of learning, teaching, practical applications of animal models, and experience.