This volume contains papers presented at a conference held in April 2007 at the CRM in Montreal honouring the remarkable contributions of John McKay over four decades of research. Papers by invitees who were unable to attend the conference are also included. The papers cover a wide range of topics, including group theory, symmetries, modular functions, and geometry, with particular focus on two areas in which John McKay has made pioneering contributions: 'Monstrous Moonshine' and the 'McKay Correspondence'. This book will be a valuable reference for graduate students and researchers interested in these and related areas and serve as a stimulus for new ideas.