The convergence of a sequence of random variables (RVs) is of central importance in probability theory and in statistics. In probability, it is often desired to understand the long term behavior of, for example, the relative frequency of an event, does it converge to a number? In what sense does it converge? In statistics, a given estimator often has the property that for large samples the values it takes are distributed around and are close to the value of the desired parameter. In many situations the distribution of this estimator can be approximated by a well known distribution, which can simplify the analysis. Thus it is necessary to understand the types of convergence of such sequences, and conditions under which they occur.