This book describes the basic elements in the theory of animal breeding and inheritance of quantitative economic traits and the way in which this technology can be implemented in selective breeding programs for aquaculture species. The role and the implementation of molecular genetics in modern selective breeding programs is also addressed. The books main objective is to stimulate development of efficient selective breeding programs in aquaculture, the worlds fastest growing industry for animal protein production. Considerable genetic gain from selection has been demonstrated for several aquatic species in traits like growth rate and survival. AKVAFORSK and allied institutions have demonstrated the value of selection in Atlantic salmon, rainbow trout, Nile tilapia, rohu carp and the shrimp Penaeus vannamei. Presently, however, less than 10 % of total world aquaculture production is based on genetically improved animals. The urgent challenge to the industry is to implement and start selective breeding programs in order to make the aquaculture industry more competitive and sustainable, through improving the utilization of feed, land and water resources. The text has been written by scientists at AKVAFORSK, Akvaforsk Genetics Center and co-workers in order to summarise present knowledge in the field, and to encourage implementation of selective breeding programs for economically important fish and shellfish species around the world.