  We analyse the renormalizability of the sine-Gordon model by the example of
the two-point Green function up to second order in alpha_r(M), the dimensional
coupling constant defined at the normalization scale M, and to all orders in
beta^2, the dimensionless coupling constant. We show that all divergences can
be removed by the renormalization of the dimensional coupling constant using
the renormalization constant Z_1, calculated in (J.Phys.A36,7839(2003)) within
the path-integral approach. We show that after renormalization of the two-point
Green function to first order in alpha_r(M) and to all orders in beta^2 all
higher order corrections in alpha_r(M) and arbitrary orders in beta^2 can be
expressed in terms of alpha_ph, the physical dimensional coupling constant
independent on the normalization scale M. We solve the Callan-Symanzik equation
for the two-point Green function. We analyse the renormalizability of Gaussian
fluctuations around a soliton solution.We show that Gaussian fluctuations
around a soliton solution are renormalized like quantum fluctuations around the
trivial vacuum to first orders in alpha_r(M) and beta^2 and do not introduce
any singularity to the sine-Gordon model at beta^2 = 8pi.
