This investigation may be summarized as follows:;The basic elements of a theory of sampling systems for finite universes has been developed in Chapter III. By considering the probabilities of including individual sampling units, pairs of sampling units, and k-tuplets of sampling units in a sample of a given number of units, the theory as developed is sufficiently general in scope to provide for both equal and unequal probability selection schemes;A general class of estimators has been introduced, the elements of which are linear functions of the variate under estimate. The coefficients of these estimators depend upon the universe units included in the sample and can be determined by imposing the condition of unbiasedness. (Abstract shortened by UMI.)