This book deals with the theory of computer arithmetic and it treats an implementation of arithmetic on digital computers. The aim is to improve the accuracy of numerical computing and to control the quality of the computed results. It illustrates how advanced computer arithmetic can be used to compute highly accurate and mathematically verified results. Basic notation and classical results are repeated in order to make the text self-contained. The book has three parts. Part 1 consists of four chapters (First concepts, Ringoids and vectoids, Definition of computer arithmetic, and Interval arithmetic) and it deals with the theory of computer arithmetic. Part 2, also comprising four chapters (Floating-point arithmetic, Implementation of floating-point arithmetic on computer, Hardware support for interval arithmetic, and Scalar products and computer arithmetic) treats implementation of arithmetic on computers. Part 3, comprising only one chapter (Sample applications), illustrates by a few applications how advanced computer arithmetic can be used to compute highly accurate and mathematically verified results. The book can be used as a high-level undergraduate textbook but also as a reference work for research in computer arithmetic and applied mathematics.