This dissertation makes use of incidence matrices and association matrices to furnish a unified treatment of Kronecker product designs. New proofs are given for a number of theorems pertaining to these designs. Also, some replacement design construction techniques are reformulated as Kronecker product designs, and new proofs are presented under the same unified treatment for the related theorems. It is also shown, inter alia, that a BIBD can not be constructed using a Kronecker product of any two block designs. In addition, a replacement theorem is given which provides conditions for reducing the numer of associate classes for a PBIBD.