The main purpose of this thesis is to study R-projectivity and max-projectivity of some classes of modules, and module classes related to max-projective modules. A right R-module M is called max-projective provided that each homomorphism f:M → R/I where I is any maximal right ideal, factors through the canonical projection π:R → R/I. We call a ring R right almost-QF (resp. right max-QF) if every injective right R-module is R-projective (resp. max-projective). In this thesis we attempt to understand the class of right almost-QF (resp. right max-QF) rings. Among other results, we prove that a right Hereditary right Noetherian ring R is right almost-QF if and only if R is right max-QF if and only if R = S x T , where S is semisimple Artinian and T is right small. A right Hereditary ring is max-QF if and only if every injective simple right R-module is projective. Furthermore, a commutative Noetherian ring R is almost-QF if and only if R is max-QF if and only if R = A x B, where A is QF and B is a small ring. Moreover, we introduced and studied some homological objects related with max-projective modules.