This elementary introduction to probability theory and information theory provides a clear and systematic foundation to the subject; the author pays particular attention to the concept of probability via a highly simplified discussion of measures on Boolean algebras. He then applies the theoretical ideas to practical areas such as statistical inference, random walks, statistical mechanics, and communications modeling. Applebaum deals with topics including discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem, and the coding and transmission of information. The author includes many examples and exercises that illustrate how the theory can be applied, e.g. to information technology. Solutions are available by email. This book is suitable as a textbook for beginning students in mathematics, statistics, or computer science who have some knowledge of basic calculus.