These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises.