Projective geometry and noncommutative algebra

In this dissertation the projective geometry of quadratic algebras is studied with particular emphasis on the computation of point modules of these algebras. Some connections to simple modules will be shown and the relationship of point modules with periodic point sequences and cyclotomic modules will be exhibited.;In the case where these algebras arise as deformations of a commutative polynomial algebra, point modules and higher dimensional analogues are investigated from the standpoint of deformation theory. Both point modules and higher dimensional analogues of point modules are seen to relate to symplectic geometric objects.;Finally the question of the geometry of lines is addressed in the case of four dimensional algebras. Weak line modules are defined and the weak line modules of an algebra defined by the rational normal curve and a plane are computed.