The aim of this paper is to elucidate the concepts of society, social group, power, class, structure, and change. This clarification is performed essentially with the help of the concepts of relation (in particular equivalence relation), set (in particular equivalence class), function, and matrix. In addition to that analysis, a framework for sociological hypotheses and theories is evolved, reminiscent of certain ideas in mathematical ecology. Thus social structure is defined as a matrix exhibiting the distribution of the total population of a community among the various social groups resulting from the partitions of the society induced by so many social equivalence relations. And social change is defined as a redistribution of the relative populations of those social groups. The advantages and limitations of this approach arc discussed. Also, a number of methodological remarks are made.