  A reformulation of the Thirring model as a gauge theory on both continuum
spacetime and discretized lattice is reviewed. In (1+1) dimensions, our result
reproduces consistently the bosonization of the massless Thirring model. In
(2+1) dimensions, the analysis by use of Schwinger-Dyson equation is shown to
exhibit dynamical fermion mass generation when the number $N$ of four-component
fermions is less than the critical value $N_{cr}= 128/3\pi^{2}$.
