ThesisIn 1932, Seifert introduced a large class of 3-manifolds, now called Seifert manifolds. In his paper, he determined the fundamental groups and homology groups of Seifert manifolds. Until the year 2000, however, the ring structures of these cohomology groups were not known apart from a few special cases. Bryden, Hayat-Legrand, Zieschang, and Zvengrowski computed the cup product structures in the cohomology of orientable Seifert manifolds with infinite fundamental group and coefficients Zr (for p prime). This dissertation is primarily devoted to carrying out the above programme for those Seifert manifolds with finite fundamental group, also known as the Clifford-Klein spherical space forms, with coefficients including both Z and 74,.