This course serves as the fundamental course of our M.Phil. and Ph.D. programs in statistics with the aim of helping postgraduate students and senior undergraduates to master some basic concepts and theories in Advanced Statistics so as to lay a solid foundation for the research in statistics. Starting from the first principles of probability theory, we develop the theory of statistical inference using calculus, statistical concepts and principles. Home works (assignments) are essential to understand the subject so I strongly encourage all the students try to ?nish them, please try first independently, if there is di?culty, consult the others, but make sure you can do them next time around. This course will cover the following topics: 1. Basic probability theory; 2. Transformations and expectations; 3 Common families of distributions; 4, Multiple random variable; 5, Properties of a random sample; 6, Principle of data reduction; 7, Point estimation and hypothesis testing; 8, Interval estimation; 9, Asymptotic evaluation.