The book covers the whole range of numerical mathematics from linear equations to ordinary differential equations with short sections on the calculus of errors and on partial differential equations. It attempts to give a unified approach of theory, algorithms, applications and use of software. Therefore it contains only a few proofs but many examples and applications.This book is appearing simultaneously with the problem-solving environment PAN. The PAN system contains an enlarged hypertext version of the text, together with all the programs described in the text, help systems, and utility tools. PAN is licensed public domain software. This parallel appearance of paper and electronic versions including additional useful software is unique.There are four appendices, which describe PAN, the programs written for PAN that are used in the text for examples and applications, and the NAG Fortran and NAG Graphics Libraries used by the programs.