Geometrical probability and statistics are poorly defined fields. But many sciences raise probabilistic and statistical problems that are inherently geometrical. (This is to be contrasted with a geometrical approach to non-geometrical problems.) In particular, Geology and Metallurgy need both stochastic models for spatial phenomena and methods of analysis for spatial data. Associated with the 38th Session of the ISI in Washington, there was a Satellite Symposium [10] at the Battelle Institute, Seattle, devoted to these problems, with particular emphasis on metals. This symposium had funds which were not available for its sequel in France, which had a more geological setting. As a result many possible speakers had to cancel at the last moment. Thus the original intent is not clearly seen from the titles of the papers. The aim was to bring together people working on the mathematical theory of random sets and those concerned with Statistical problems where this theory could be helpful. It was natural to hold the Symposium at the Centre de Morphologie Mathematique since pioneering work in this whole area was done there. The concept of a random set unifies geometric probability and many parts of probability theory and analysis. Statisticians are very familiar with F (x) = prob {X<x}. If we think of X as a random set (one point) on the real line and I(-,, x as the interval from co up to and including x, we know all about X if we know prob {X e I(-_, x3 }, for all x. To characterize a more general random set X, in say Rn, we will need analogously to know probabilities like prob (Xc B), prob (X nB = b) for many fixed sets B. This formulation arose naturally (in the early '60s both in France and America) in the examination of sections of a sedimentary rock by a flying-spot scanner. The set X are those points in the plane occupied by sand grains and B may be thought of as the section of the light beam the full light signal passes through if X nB = 0. This same application suggests the concept of a stationary random set since this corresponds to our idea of a homogeneous sediment. The precise mathematical formulation is rather difficult. The key result is due to Choquet [3], who showed that for a random closed set (RACS) X and compact sets B, prob {XnB 0' D } = T (B) must be a capacity and conversely. Many familiar results from probability theory reappear in most interesting forms. For example, a RACS X is infinitely divisible if it may be expressed for any n as the union of n independent RACS. Again a RACS X is stable under unions, if for any n there