This book is meant for Undergraduate (Hons./Major) and Postgraduate students of Statistics and Mathematics. Mathematical Statistics has become a major tool of research in different natural, physical and social sciences. This book gives a systematic exposition of the theory of Mathematical Statistics as is required at the Undergraduate (Honours) and Postgraduate courses in Statistics and Mathematics. The basic requirement for reading this book is knowledge in Mathematics up to the graduation level including a course in Calculus. The ideas have been illustrated with a large number of examples at each step and supplemented by a number of exercises. The research students in statistics may also find parts of the book useful.