In this book we cover the essentials of the foundations of statistical modeling. We begin with the concepts and properties of statistical distributions, and describe important properties of the various frequently encountered distributions as well as some of the more exotic but useful ones. We have an extensive section on matrix properties that are fundamental to many of the algorithmic techniques we use in modeling. This includes sections on unusual yet useful methods to split complex calculations and to iterate with the inclusion/exclusion of specific data points. We describe the characteristics of the most common modeling frameworks, both linear and nonlinear. Time series or forecasting models have certain idiosyncrasies that are sufficiently special so we devote a chapter to these methods.