This book is a revised version of the author's PhD thesis. It describes the stochastic process algebra PEPA (Performance Evaluation Process Algebra) that is suitable for use in a number of performability modelling situtuations. PEPA expands on "classical" process algebras such as CCS and CSP by incorporating stochastic delays between state transitions. This book is a good introduction to the field of Stochastic Process Algebra and would be a useful addition to anyone interested in performance modelling who wishes to gain understanding of this exciting new approach.