Let M be a closed orientable 2n-dimensional -manifold such that n , 2 and M is either (n􀀀2)-connected or (n􀀀1)-connected. Such a manifold M can be decomposed as a connected sum of certain simpler manifolds. In this thesis, by using such connected sum decompositions, we develop multiplicative gluing formulas that express the Reidemeister torsion of M with untwisted R-coecients in terms of Reidemeister torsions of its building blocks in the decomposition. Then we apply these results to handlebodies, compact orientable smooth (2n+1)-dimensional manifolds whose boundary is a (n􀀀2)-connected 2n-dimensional closed -manifold, and product manifolds.