Nowadays, breeding of high productive farm animals, like cattle, pigs and poultry is in the hands of multinational companies which invest a lot of money in state of the art breeding programs. The breeding of sheep, goats, horses and companion animals, e.g. the dog are based on individual breeders collaborating in the setting of a herd book or a breeder's association. Animal breeding is aiming at the improvement of animals by changing their genetic abilities for important traits. These traits are determined by the requirements and wishes from the society which might change over time. Animal breeding is highly influenced by research and developments in population-, quantitative- and molecular genetics. Sometimes, unexpected negative effects of animal breeding are observed that require adequate corrections. This text provides a useful overview for those new to the field of animal genetics and breeding, covering a diverse array of relevant topics on the subject. The book will be highly useful for graduate students of Veterinary sciences having little or no background in Veterinary genetics.