Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appears here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations.

• 1. Abstract reduction systems
• 2. First-order term rewriting systems
• 3. Examples of TRSs and special rewriting formats
• 4. Orthogonality
• 5. Properties of rewriting: decidability and modularity
• 6. Termination
• 7. Completion of equational specifications
• 8. Equivalence of reductions
• 9. Strategies
• 10. Lambda calculus
• 11. Higher order rewriting
• 12. Infinitary rewriting
• 13. Term graph rewriting
• 14. Advanced ARS theory
• 15. Rewriting based languages and systems
• 16. Mathematical background.