An updated new edition of the popular elementary introduction to probability theory and information theory, now containing additional material on Markov chains and their entropy. Suitable as a textbook for beginning students in mathematics, statistics, computer science or economics, the only prerequisite is some knowledge of basic calculus. A clear and systematic foundation to the subject is provided; the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics discussed include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information. Many examples and exercises illustrate how the theory can be applied, for example, to information technology. Detailed solutions to most exercises are available on the web.