This is a final report, for administrative purposes, of studies to be published in the general category of mathematical theory of social groups, with emphasis on the large groups typical of educational communities. Since the study of the large and complicated structures of high school and college communities is difficult by purely empirical methods, they must be represented by mathematical and computer models. Beginning work on such models was the principal activity under the project grant. Abbreviated titles of working papers in the project include: "On the Structure of Large Groups,""The Construction of a Miniature Community,""A Theoretical Framework for the Analysis of Affective Structure,""Sampling Social Structure,""Sociological Applications of Incidence Matrices,""Indifference in Balance Theory," and "Youth Culture." Publication plans for the final versions of these and other working papers in the project will be available by winter, 1972-73, from the Institute of Behavioral Science, University of Colorado. (BW/Author)