Abstract: The arithmetic of transfinite cardinal numbers is one of the fundamental issues of set theory. This talk will give an overview of most of what is known about cardinal arithmetic. We will first cover ordinals, cardinals, and the classical results on cardinal exponentiation. Next, we will look at PCF Theory, the modern method developed to obtain further bounds on cardinal exponents. But this theory is also interesting in its own right, so we will conclude with a problem or two in PCF Theory.