This book originated from a series of lectures and seminars at the University of Saarbrücken. It contains a comparative description of fast and cost-effective algorithms for performing arithmetic operations in digital computers. Although almost all computer scientists and not a few scientists from other disciplines are confronted with these problems to varying degrees, German-language technical books with a more general focus only address these issues tangentially or in relatively short chapters; this inevitably leads to a limitation to the description of the most well-known and simplest methods. While there are several excellent standard works in the English literature (notably Flores' "The Logic of Computer Arithmetic"), these are often difficult to access and mostly of older date.