The generalized stereographic projection and inversion

This thesis is divided into six sections. In the first section, basic notions are given. In the second and third sections, the stereographic projection and inversion are devoted for n-dimensional pseudosphere with index v, respectively. Stereographic projection and inversion of n-dimensional pseudohyperbolic space with index v are obtained in the fourth and fifth sections which are original parts of the thesis. Finally, in the 3 dimensional hyperbolic space, the images under stereographic projection of some special surfaces are visualized in three dimensional Euclidean space.