This book is intended to introduce the reader to the important practical problem of solving large systems of sparse linear equations on a computer. The problem has many facets, from fundamental questions about the inherent complexity of certain problems, to less precisely specified questions about the design of efficient data structures and computer programs. In order to limit the size of the book, and yet consider the problems in detail, we have restricted our attention to symmetric positive definite systems of equations. Such problems are very common, arising in numerous fields of science and engineering. For similar reasons, we have limited our treatment to one specific method for each general approach to solving large sparse positive definite systems. For example, among the numerous methods for approximately minimizing the bandwidth of a matrix, we have selected only one, which through our experience has appeared to perform well. Our objective is to expose the reader to the important ideas, rather than the method which is necessarily best for his particular problem. Our hope is that someone familiar with the contents of the book could make sound judgements about the applicability and appropriateness of proposed ideas and methods for solving sparse systems.