New geometric structures designed on manifolds modeled on frechet algebra without norm

This thesis consists of four parts. In the first chapter, the basic definitions and theorems that will be used throughout the thesis are given. The second chapter is divided into two sections, in the first section we define a new class of topological algebra which we call convenient algebra by using and generalizing the method of convenient topological vector spaces, and in the second one designed a new manifold by considering these algebras as model space of these manifolds. In the third chapter, we studied and discussed the mappings between these manifolds that constructing in the second chapter. Chapter four deals with conclusions and future works.