English : This thesis is based on the works done by M . Behboodi , A . Ghorbani , A . Moradzadeh , S . H . Shojaee and Noyan Er. Let R is an associative ring with identity . A left (or right) K?the ring is a ring R such that each left (or right) R-module is a direct sum of cyclic submodules . A ring R is called a K?the ring if it is both left and right K?the ring . K?the proved that over an Artinian principal ideal ring , each module is a direct sum of cyclic modules . Furthermore , if a commutative Artinian ring has the property that all its modules are direct sums of cyclic modules , then it is necessarily a principal ideal ring . Later Cohen and Kaplansky obtained this result that If R is a commutative ring such that each R-module is a direct sum of cyclic modules then R must be an Artinian principal ideal ring . Thus by combining results above one obtains that A commutative ring R is a K?the ring if and only if R is an Artinian principal ideal ring . First In this thesis , we obtain a partial solution to the question of K?the ``For which rings R is it true that every left (or left and right) R-module is a direct sum of cyclic modules?'' Let R be a ring in which all idempotents are central (for example R is duo-ring or local ring or uniform ring) . It is shown that , if R is a left K?the ring then R is an Artinian principal right ideal ring . Next we conclude that R is K?the ring if and only if is an Artinian principal ideal ring . Also it is shown that if R= is a finite product of rings R i such that for each i, Ri R i is uniform , then R is a K?the ring if and only if R is a left K?the ring if and only if R is an Artinian principal ideal ring if and only if R is isomorphic to a finite product of Artinian uniserial rings . Second we study rings whose modules are direct sums of extending modules . A module M is called extending if every submodule of M is essential in a direct summand of M. We will prove that such rings are precisely the rings of finite type and right colocal type , so that they are Artinian , right (but not necessarily left) serial and every right R-module is a direct sum of uniform modules . Artinian serial rings introduced by Asano and K?the is an important Also , rings of right invariant module type and finite dimensional algebras (over a field) of left local type are among examples of rings whose modules are direct sums of extending modules .Since K?the rings and rings whose modules are direct sums of extending modules have proximate relation together , for example Artinian serial rings are K?the ring , hence We study them together .