This thesis is based on the article " Second Modules over Noncommutative Rings " written by S . Ceken , M . Alkan , and P . F . Smith . The notion of second modules and second submodules introduced by Yassemi , which is a dual to the notion of prime modules . Let R be an arbitrary ring . A nonzero unital right R-module M is called a second module if M and all its nonzero homomorphic images have the same annihilator in R. A nonzero unital right R-module M is called a prime module if M and all its nonzero submoduls have the same annihilator in R. By a prime submodule of a right R-module M we mean a submodule N such that the module M/N is prime . By a second submodule of a module we mean a submodule which is also a second module . Let R be a commutative ring, and let M be a nonzero R -module. Given any element r R , let :M M denote the endomorphism of M defined by (m) = r.m (m M) . It is easy to check that M is prime if and only if for each r R either is zero or a monomorphism. In other words, M is prime if and only if for any r in R and m in M, r.m = 0 implies that m = 0 or rM = 0. On the other hand, the R- module M is second if and only if for each r R either is zero or an epimorphism. Putting it another way, M is second if and only if for any r in R , either r.M = 0 or r.M = M .