Dey, Arindam2019-10-232023-10-202019-10-232023-10-202019ROLL NO.11612312https://gyan.iitg.ac.in/handle/123456789/1385Supervisor: Vinay WaghThe goal of this thesis is to study module of derivations of certain rings of invariants and of certain hypersurface rings. The thesis is divided into two parts.In the rst part we study module of derivarions of ring of invariants under the linear action of cyclic subgroups of GL(n; k). The motivation to study this comes from a result by R. V. Gurjar and V. Wagh. They have proved [2] that for a nite cyclic subgroup G of GL(2;C) the module of derivations of the ring of invariants is minimally generated by 4 elements.enMATHEMATICSThesis