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The book provides a solid, well-thought and well-balanced foundation in probability and statistical inference enabling the students to gain fundamental understanding of the subject. The material will be presented in a way so as to invoke thinking process in students, and help students in finding solutions to problems posed to them. Mathematics is required for understanding probability, and probability is needed to understand statistical inference. Fisher presented a way to introduce methodologies, and lay foundations in statistics while Neyman showed a way how mathematics should be used in statistics to prove things mathematically, and brought mathematical orientation in statistics. This book is a humble attempt to accomplish a gigantic task of incorporating both Fisher's, and Neyman's approaches by way of introducing methodologies with precise mathematical setup which can stand up to any mathematical settings. Topics covered in the book will be fairly conventional along with some recent topics in probability and statistical inference presented in a rigorous mathematical and conceptual way. The aim of the book is to use principles of probability theory, using tools of measure theory to build strong theoretical statistical inference. The topics will have wealth of material, and many topics will be given greater in-depth coverage. The conceptual structure of topics will be self-contained. Methodology will be illustrated using real-life applications. Proofs will be provided for almost all the theorems and statements. 2. Material will be backed by well-researched references. 3. More than 500 problems will be provided. 4. More than 300 worked out examples will be provided. 5. R code for most of the worked out examples will be provided in the text. 6. Numerous figures and tables will be used to help in understanding the concepts.