This textbook has been developed from the lecture notes for a one-semester course on stochastic modelling. It reviews the basics of probability theory and then covers the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. Rigorous proofs are often replaced with sketches of arguments--With indications as to why a particular result holds, and also how it is connected with other results--and illustrated by examples. Wherever possible, the book includes references to more specialised texts containing both proofs and more advanced material related to the topics covered. Contents: Basics of Probability Theory; Markov Chains; Markov Decision Processes; The Exponential Distribution and Poisson Process; Jump Markov Processes; Elements of Queueing Theory; Elements of Renewal Theory; Elements of Time Series; Elements of Simulation. Readership: Upper level undergraduates, graduate students, lecturers and researchers in probability theory and stochastic processes.