This book has evolved out of lecture courses delivered to Research Scholars at the Tata Institute of Fundamental Research during the period 1978-88. It attempts to provide a practical guide for numerical solutions to mathematical problems on digital computers. It is intended for both students and research workers in science and engineering. Readers are expected to have a reasonable background in mathematics as well as computer programming.The enormous variety of problems that can be encountered in practice makes numerical computation an art to some extent, and as such the best way of learning it is to practice it. Attempting to learnnumerical methods by simply attending lectures or by just reading a book is like trying to learn how to play football by the same method. All students are therefore urged to try out the methods themselves on any problem that they may fancy, not necessarily the ones given in this book. In fact, the reader will probably not appreciate the contents unless he makes a serious attempt to usenumerical methods for solving problems on computers.