This book analyses the geometrical aspects of the simplicial quantum gravity model known as the dynamical triangulations approach. A compact and convenient account is given both to introduce the non-expert reader to the spirit of the subject and to provide a well-chosen mathematical route to the heart of the matter for the expert. The techniques described are novel and allow points of current interest in the subject of simplicial quantum gravity to be addressed. Linear manifolds and entropy estimates of the number of triangulations of 3and 4-manifolds are discussed. Continuum physics is recovered through scaling limits and computer simulation is used to study simplicial quantum gravity extensively. The beginner will appreciate the introduction to the field, the expert a comprehensive account of recent results and developments.