Weak-injective modules over commutative rings have been defined by Lee as modules M which satisfy (A,M)=0 for all R-modules A of weak dimension ? 1. In this thesis based o [10] and [11] it is shown that type="#_x0000_t75" of modules weak dimension ? 1 and the ( ). In general, the type="#_x0000_t75" (U,N)=0 for any R-module N implies that N is weak-injective. We study weak-injective envelopes of modules and we show that all R-modules admit weak-injective envelope, i.e., every R-module can be embedded in a weak-injective module with cokernel of weak dimension ? 1. In particular it is shown that if R is a commutative domain and Q (? R) it is field of quotients then for the weak-injective envelope of an R-module N, it is a direct sum of copies of Q if and only if N is a flat R-module. Also, it is shown that there is a close relation between the flat cover (whose existence is guaranteed by well-known theorem of Bican, El Bashir and Enochs [26]) and the weak-injective envelope of any R-module. This yield a method of constructing weak-injective envelopes from flat covers (and vice versa). This relation can be best illustrated by the diagram in Theorem 5.35. Similar relation exists between the Enochs-cotorsion envelopes and the weak dimension ? 1 covers of modules. Over a coherent domain, the cokernel of an arbitrary Enochs-cotorsion module in it is weak-injective envelope is always pure-injective. A ring R almost perfect if all proper factor rings of R are perfect. Almost perfect domains can be characterized in several ways, one of which is that the concepts of Matlis-cotorsion and Enochs-cotorsion coincide. These domains have already been the topics of several research papers. One of our main purposes is to add new characterizations in terms of weak-injectivity. So it is introduced the global weak-injective dimension of a domain R. It turns out that this dimension is equal to the supremum of projective dimension of R-modules of weak dimension 1. A main result is Theorem 6.14 stating that a domain R is almost perfect if and only if its global weak-injective dimension is 1. This yields several other possibilities for characterizing almost perfect domai cf. Corollary 6.20. H-divisible pure-injective R-modules are always weak-injective, but the converse is not true whenever R is an almost perfect, non-Dedekind domain.