These lecture notes are organized into six modules. Module one is about Distribution Theory, module two is on the Joint Probability Distributions and module three covers Exact Sampling Distributions. The lecture notes proceed with module four whereby the Bivariate Normal Distribution is presented followed by module five on Inferential Statistics. The lecture notes completes with module six on Non Parametric Hypothesis Testing. The Author is of the opinion that, a user to these lecture notes must have accessed any book in elementary statistics and at least has a strong background in advanced mathematics, otherwise, he/she may find it very difficult to digest the materials included. It is my hope that, students in statistics will enjoy following the notes as supplementary materials to what they are actually going to get during lecture contacts in their classes.