This book is aimed at the numerate reader who has probably taken an introductory statistics and probability course at some stage and would like a brief introduction to the core methods of statistics and how they are applied, not necessarily in the context of standard models. The first chapter is a brief review of some basic probability theory needed for what follows. Chapter 2 discusses statistical models and the questions addressed by statistical inference and introduces the maximum likelihood and Bayesian approaches to answering them. Chapter 3 is a short overview of the R programming language. Chapter 4 provides a concise coverage of the large sample theory of maximum likelihood estimation, and Chapter 5 discusses the numerical methods required to use this theory. Chapter 6 covers the numerical methods useful for Bayesian computation, in particular Markov chain Monte Carlo. Chapter 7 provides a brief tour of the theory and practice of linear modelling. Appendices then cover some useful information on common distributions, matrix computation and random number generation. The book is neither an encyclopedia nor a cookbook, and the bibliography aims to provide a compact list of the most useful sources for further reading, rather than being extensive. The aim is to offer a concise coverage of the core knowledge needed to understand and use parametric statistical methods and to build new methods for analysing data. Modern statistics exists at the interface between computation and theory, and this book reflects that fact. I am grateful to Nicole Augustin, Finn Lindgren, the editors at Cambridge University Press and the students on the Bath course ‘Applied Statistical Inference’ and the Academy for PhD Training in Statistics course ‘Statistical Computing’ for many useful comments.