In this thesis, we present an expanded account of Baer modules based on anarticle bye S.Tariq Rizvi and Cosmin S.Roman in 2009. We assume that R is a ring (not necessarily commutative) with unity and is an unital right module. The concept of Baer rings have been the focus of a number of research papers. A ring is called Baer if the right annihilator of any nonempty subset of is generated by an idempotent. This concept has it's root in functional analysis having close links to C* -algebras and von-Neuman regular rings and the endomorphisms rings of semisimple modules, are examples of Baer rings. Let End( ) be the ring of endomorphisms of . A right module is called a Baer module if the right annihilator in of any left ideal of is generated by an idempotent of . Chatters and Khuri in howed that every right nonsingular right extending ring can be characterized as a Baer ring which is right cononsingular