The development of the use of computers and software in art from the Fifties to the present is explained. As general aspects of the history of computer art an interface model and three dominant modes to use computational processes (generative, modular, hypertextual) are presented. The "History of Computer Art" features examples of early developments in media like cybernetic sculptures, computer graphics and animation (including music videos and demos), video and computer games, reactive installations, virtual reality, evolutionary art and net art. The functions of relevant art works are explained more detailed than usual in such histories. The German version was completed in December 2012. The last chapter of the English translation was published in June 2014. First update: September 2015.