Term rewriting is a branch of theoretical computer science which combines elements of logic, universal algebra, automated theorem proving and functional programming. Its foundation is equational logic. What distinguishes term rewriting from equational logic is that equations are used as directed replacement rules, i.e. the left-hand side can be replaced by the right-hand side, but not vice versa. This constitutes a Turing-complete computational model which is very close to functional programming. It has applications in algebra (e.g. Boolean algebra, group theory and ring theory), recursion theory (what is and is not computable with certain sets of rewrite rules), software engineering (reasoning about equationally defined data types such as numbers, lists, sets etc.), and programming languages (especially functional and logic programming). In general, term rewriting applies in any context where efficient methods for reasoning with equations are required.

To date, most of the term rewriting literature has been published in specialist conference proceedings (especially Rewriting Techniques and Applications and Automated Deduction in Springer's LNCS series) and journals (e.g. Journal of Symbolic Computation and Journal of Automated Reasoning). In addition, several overview articles provide introductions into the field, and references to the relevant literature [141, 74, 204]. This is the first English book devoted to the theory and applications of term rewriting. It is ambitious in that it tries to serve two masters:

• The researcher, who needs a unified theory that covers, in detail and in a single volume, material that has previously only been collected in overview articles, and whose technical details are spread over the literature.

• The teacher or student, who needs a readable textbook in an area where there is hardly any literature for the non-specialist.