This book is designed as a text to be used in a course on the NAG Fortran Library of mathematical software routines. It concentrates mainly on the software and its use and not on the underlying numerical methods. The text consists of three parts.

First, there is a discussion of some of those aspects of FORTRAN with which inexperienced users often have difficulty. For example, subroutine parameters and multidimensional array parameters are discussed in detail. Also, sample NAG routine documentation for a variety of applications is thoroughly analyzed.

Second, a variety of easy-to-use routines from the NAG library are considered. These aim to solve problems arising in Fourier transforms, quadrature, ordinary differential equations, curve fitting, optimization, linear algebra, statistics, sorting, and special functions. Also, a number of the simpler subroutines from the NAG Graphical Supplement are described. For each routine considered, the parameters are carefully discussed. This includes a thorough treatment of the error exits. Then, the construction of an on-line program to call the routine is shown, and the results of a sample run of that program are given.

Finally, a general strategy for using the NAG Library is discussed. The reader is shown how to use the Library manual and the chapter-by-chapter flowcharts. Examples of a variety of more comprehensive routines than those considered earlier in the text are used to show how to call almost any routine in the Library. The problems considered here are mainly more difficult or more specific than those discussed earlier (e.g., multiple integration). However, the reason for this choice is to illustrate the general use of routines from the Library rather than to provide a recipe for the particular problem.

Overall, the text represents a worthy attempt at introducing the inexperienced user of mathematical software to the NAG Library. It would be particularly suitable as a text accompanied by another on the underlying numerical methods.