Summary: ``In this paper, we investigate the notions of $\Cal X^\bot$-projective, $\Cal X$-injective, and $\Cal X$-flat modules and give some characterizations of these modules, where $\Cal X$ is a class of left modules. We prove that the class of all $\Cal X^\bot$-projective modules is Kaplansky. Further, if the class of all $\Cal X$-injective $R$-modules is contained in the class of all pure projective modules, we show the existence of $\Cal X^\bot$-projective covers and $\Cal X$-injective envelopes over a $\Cal X^bot$-hereditary ring. Further, we show that a ring $R$ is Noetherian if and only if $\Cal W$-injective $R$-modules coincide with the injective $R$-modules. Finally, we prove that if $\Cal W \subseteq S$, every module has a $\Cal W$-injective precover over a coherent ring, where $\Cal W$ is the class of all pure projective $R$-modules and $\Cal S$ is the class of all $fp - \Omega^1$-modules.''