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This dissertation is devoted to investigations in the theory of Rickart modules. We introduce various notions related to the Rickart property in a general module theoretic setting. Endomorphism ring of a module plays an important role in our study. Topics of our study include: Rickart modules, dual Rickart modules, endoreg-ular modules and endo-Rickart modules. These notions constitute the main chapters of the dissertation. A module M is called Rickart if the right annihilator in M of any single element of S = EndR(M) is generated by an idempotent of S. This extends the notion of a Baer module as well as that of a right Rickart ring. M is called a dual Rickart module if the image in M of any single element of S is generated by an idempotent of S. M is called an endoregular module if its endomorphism ring is von Neumann regular. M is called an endo-Rickart module if the left annihilator in S of any single element of M is generated by an idempotent in S. We provide several characterizations and investigate properties of each of thes