This book is designed for a beginning or an intermediate graduate course in stochastic modelling. It is intended for a serious student in probability theory, statistics, actuarial sciences or financial mathematics. The overall objective is to make the basic concepts of stochastic modelling and insurance accessible to students and research workers in a comprehensive manner. Renewal theory, random walks, discrete and continuowtime Markov processes, martingde theory and point processes are among the major subjects treated. The selection of the topics has been largely made on the basis of their relevance within an actuarial or financial context. In this sense, the book is rather special. On the other hand, one could have written a similar textbook but with queueing theory or stochastic networks as the scrutinizing subject.