Includes bibliographical references (p. [293]-296) and index.

1. Algebraic Preliminaries -- 2. Integration of Rational Functions -- 3. Differential Fields -- 4. The Order Function -- 5. Integration of Transcendental Functions -- 6. The Risch Differential Equation -- 7. Parametric Problems -- 8. The Coupled Differential System -- 9. Structure Theorems. This book, the first volume in the new series Algorithms and Computation in Mathematics, is bound to become the standard reference for symbolic integration. The author is the leading expert on this topic and his book is the first book to treat it comprehensively and in detail including new results. Many algorithms are given in pseudocode and, hence, can be implemented. The book addresses mathematicians and computer scientists who are interested in symbolic computation, developers and programmers of computer algebra systems and users of symbolic integration methods. It will also serve as a textbook to be used for lecture courses on symbolic integration.