Some elementary concepts of statistics and probability are reviewed, including convergence concepts. Then the concepts of sufficiency, likelihood, and information are introduced. Several methods of estimation, such as maximum likelihood estimation and Bayes estimation, are studied, and some approaches to comparing different estimation procedures are discussed. The class also covers tests of hypotheses, and for both estimation and testing, methods for finding and characterizing optimal decisions are considered. Additional topics are covered depending on time and interest. Material is presented at the level of Bickel and Doksum, Mathematical Statistics, and Casella and Berger, Statistical Inference.