A basic course in statistical theory covering standard statistical methods and their applications. Includes unbiased, maximum likelihood, and moment estimation; confidence intervals and regions; testing hypotheses for standard distributions and contingency tables; and introduction to nonparametric tests and linear regression. Modern statistical concepts and methods developed in a mathematical framework: statistical inference, decision theory, point and interval estimation, hypothesis testing, Neyman-Pearson theory, maximum likelihood, Bayesian analysis, large sample theory.