This book provides an introduction to the theory and practice of Monte Carlo and Simulation methods. It arises from a 20 hour course given simultaneously to two groups of students. The first are final year Honours students in the School of Mathematics at the University of Edinburgh and the second are students from Heriot Watt and Edinburgh Universities taking the MSc in Financial Mathematics. The intention is that this be a practical book that encourages readers to write and experiment with actual simulation models. The choice of programming environment, Maple, may seem strange, perhaps even perverse. It arises from the fact that at Edinburgh all mathematics students are.