Traditional numerical analysis books concentrate either on the mathematical or programming aspects of numerical algorithms. This textbook emphasizes the relevance of these techniques to the real world and the use of a widely available library of numerical software in their application. The book consists of 22 graded projects which lead the reader through the techniques taught as part of a first course in numerical analysis. Throughout, the reader is presented with projects which reflect real problems that occur in science and industry, at the same time, becoming accustomed to using a library of numerical software when writing programs. It is a theme of this book that the use of a solid, robust and bug-free software library will improve computational results and minimize the effort of programming. By integrating the use of the NAG (Numerical Algorithms Group) FORTRAN library into the projects, students will develop experience in the use of a software library and, by practical example, be prepared for working further with numerical analysis libraries. This text aims to provide a complement to traditional numerical analysis books. Answers to exercises are included as well as full documentation of the library routines used.