This book is intended for a one or two semester course in compiling theory at the senior or graduate level. It is a theoretically oriented treatment of a practical subject. Our motivation for making it so is threefold. In an area as rapidly changing as Computer Science, sound pedagogy demands that courses emphasize ideas, rather than implementation details. It is our hope that the algorithms and concepts presented in this book will survive the next generation of computers and programming languages, and that at least some of them will be applicable to fields other than compiler writing.Compiler writing has progressed to the point where many portions of a compiler can be isolated and subjected to design optimization. It is important that appropriate mathematical tools be available to the person attempting this optimization.Some of the most useful and most efficient compiler algorithms, e.g. LR(k) parsing, require a good deal of mathematical background for full understanding. We expect, therefore, that a good theoretical background will become essential for the compiler designer.While we have not omitted difficult theorems that are relevant to compiling, we have tried to make the book as readable as possible. Numerous examples are given, each based on a small grammar, rather than on the large grammars encountered in practice. It is hoped that these examples are sufficient to illustrate the basic ideas, even in cases where the theoretical developments are difficult to follow in isolation.