Operator stable probability measures: an overview

We present an introduction to the theory of operator stable probability measures by providing an outline of the main results to date. The theory of operator stable probability measures is an extension to higher dimensional spaces of the classical theory of stable measures on the line. By departing from the historical order of development we are able to give a streamlined presentation of the key results in the theory. A new result about simultaneous centering of the symmetry group and the operator stable measure itself is included.