What is high dimensional probability? Under this broad term this text presents a collection of topics associated by the fact that n plays a key role in each whether the idea of high dimension n 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 regularly of stochastic processes, and the theory of concentration of measure. Many of the ideas, results and directions of this evolving field were explored on a broad front at the Conference on High Dimensional Probability held at Obwerwolfach in August 1996.