  Recently, Yekutieli introduced projective dimension and injective dimension
of DG-modules by generalizing the characterization of projective dimension and
injective dimension of ordinary modules by vanishing of Ext-group. In this
paper, we introduce DG-version of projective resolution and injective
resolution for DG-modules over a connective DG-algebra which are different from
known DG-version of projective and injective resolutions. An important feature
of these resolutions is that, roughly speaking, the "length" of these
resolutions give projective or injective dimensions. We show that these
resolutions allows us to investigate basic properties of projective and
injective dimensions of DG-modules. As an application we introduce the global
dimension of a connective DG-algebra and show that finiteness of global
dimension is derived invariant.
