This book presents an introduction to probability and mathematical statistics and it is intended for students already having some elementary mathematical background. It is intended for a one-year junior or senior level undergraduate or beginning graduate level course in probability theory and mathematical statistics.The book contains more material than normally would be taught in a one-year course. This should give the teacher flexibility with respect to the selection of the content and level at which the book is to be used. This book is based on over 14 years of students in senior level calculus based courses in probability theory and mathematical statistics.