||In this thesis, we discussed general Riemann-Stieltjes integrability. First, we reviewed the results of L.C.Young (1936), which concerned sufficient conditions on the existence of general Riemann-Stieltjes integrals. Second, this result is generalized. Then, given f of p-bounded variation and g of q-bounded variation with 1/p +1/q > 1, a necessary condition for the general Riemann-Stieltjes integrability is obtained. Finally, we extend that necessary result to the case of n-dimensional spaces.