This course is intended for Ph.D. students in biostatistics. The course will begin with a review of basic mathematical concepts: probability and measure, integration, modes of convergence. A decision theoretical approach to statistical inference will be introduced. In statistical estimation theory, topics such as families of distributions, point estimation, unbiasedness, algorithmic issues, etc. will be included. In hypothesis testing the Neyman-Pearson theory, unbiased tests, permutation tests, and likelihood based tests will be discussed in depth. In asymptotics, limit theorems, relative efficiency, Wald's statistic, Rao's score statistic, etc. will be discussed. An overview of robust statistical procedures will be provided.