Combinatorial group theory

Drawing on lecture courses given at the University of London, this text makes the case for bringing topology into the study of groups defined by generators and relations. Its foundation is the fundamental groupoid, which supports proofs that are both more powerful and more economical than the conventional versions.

A large part of the book is devoted to covering spaces and complexes. The author applies this technique to derive the major subgroup theorems of Schreier and Kurosh.

The later chapters present Bass-Serre theory in full and examine the word problem, including its unsolvability and Higman's Embedding Theorem. The necessary results from computability theory are also included so the material is self-contained.