What is high dimensional probability? Under this broad term one finds a collection of topics associated by the fact that plays a key role in each, whether the idea of high dimension is expressed in the problem or in the methods by which it is approached. For example, the study of probability in Banach spaces gave impetus to a number of methods whose importance has gone far beyond the original goal of extending limit laws to the vector valued case. Familiar applications are in the areas of empirical processes, the use of majorizing measures to study regularity of stochastic processes, and the...