Writing primarily for graduate-level students but also for anyone interested in group theory or dynamical systems, Nekrashevych describes groups generated by automata that are easily defined but tend to have unusual characteristics such as nontrivial torsion and intermediate growth. He covers the basic definitions and gives examples such as groups acting on rooted trees, the Grigorchuk group, and Branch groups, algebraic theory, limit spaces, orbispaces, and iterated monodromy groups. In a very interesting series of examples Nekrashevych examines the expanding self-coverings of orbifolds, limit spaces of free Abelian groups, rational functions, combinatorial equivalence and Thurston's Theorem, Hubbard's "twisted rabbit" question, topological polynomials and critical portraits, quadratic polynomials, and examples of iterated monodromy groups of polynomials. Annotation ©2005 Book News, Inc., Portland, OR (booknews.com)