Almost all of our math classes make use of the real numbers as well as subsets (the rational numbers, the integers, the natural numbers) and occasionally supersets (the complex numbers). John Horton Conway, in his research on game theory, came up with the notion of Surreal Numbers, an ordered field that contains the real numbers and much more, including positive numbers smaller than every positive real numbers (positive infinitesimals) and numbers bigger than every positive real number (positive infinite numbers). This talk will introduce the main concepts behind the Surreal Numbers, including their connection to game theory and how the real numbers are themselves defined.