  We describe two distinct approaches for bosonization in higher dimensions;
one is based on a direct comparison of current correlation functions while the
other relies on a Master lagrangean formalism. These are used to bosonise the
Massive Thirring Model in three and four dimensions in the weak coupling regime
but with an arbitrary fermion mass. In both approaches the explicit bosonised
lagrangean and current are derived in terms of gauge fields. The complete
equivalence of the two bosonization methods is established. Exact results for
the free massive fermion theory are also obtained. Finally, the two-dimensional
theory is revisited and the possibility of extending this analysis for
arbitrary dimensions is indicated.
