Aimed at advanced undergraduate and graduate students in mathematics and related disciplines, this book presents the concepts and results underlying the Bayesian, frequentist and Fisherian approaches, with particular emphasis on the contrasts between them. Contemporary computational ideas are explained, as well as basic mathematical theory. Written in a lucid and informal style, this concise text provides both basic material on the main approaches to inference, as well as more advanced material on modern developments in statistical theory, including: contemporary material on Bayesian computation, such as MCMC, higher-order likelihood theory, predictive inference, bootstrap methods and conditional inference. It contains numerous extended examples of the application of formal inference techniques to real data, as well as historical commentary on the development of the subject. Throughout, the text concentrates on concepts, rather than mathematical detail, while maintaining appropriate levels of formality. Each chapter ends with a set of accessible problems.