In algebraic geometry we study schemes as main objects . One of the most important tools in this way is to use cohomology . One can compute cohomology in a few different manners , one of them is by using derived functors . Based on a result in category theory , every object in an abelian category $\\mathcal{C}$ has an injective envelope . So every object in such a category has an injective resolution which can be used to compute cohomology . Since the category of quasi-coherent sheaves on a scheme $X$ is an abelian category , every quasi-coherent sheaf has an injective envelope . Dually we expect that every object in such a category has a projective cover , but there exists categories with no projective object except zero . Hence this expect does not occur . Edgar Enochs by noticing to treatments of flat modules asked about the existence of flat covers for every $R$-module (called Flat Cover Conjecture denoted by FCC) . This conjecture is proved in 2001 . Since in the category of quasi-coherent sheaves , $\\mathfrak{Qco}(X)$ there does not exist enough projective in general , and since quasi-coherent sheaves on a scheme play the role of modules over a ring , the study of FCC came in progress . The conjecture was proved by Enochs and Estrada in 2005 . Based on a dual relation between flat modules and absolutely pure modules , we decided to study absolutely pure modules . A part of this thesis is devoted to study these objects in $\\mathfrak{Qco}(X)$ . It is proved that over a locally coherent scheme $X$ , this class of quasi-coherent sheaves is a covering class . Also a dual relation between flat and absolutely pure sheaves is shown . Moreover , by noticing to the close relation between $\\mathfrak{Qco}(X)$ and ${\\rm Rep}(Q)$ where $Q$ is a quiver associated to scheme $X$ , we have tried to study absolutely pure representations . Some expected results about absolutely pure representations is presented . In the other part of the thesis the class of torsion free quasi-coherent sheaves is considered . It is proved that this class of quasi-coherent sheaves over an integral noetherian scheme is a covering class . Also the structure of torsion free covers of quasi-coherent sheaves over such a scheme is characterized .