  Using the algebraic Bethe ansatz method, and the solution of the quantum
inverse scattering problem for local spins, we obtain multiple integral
representations of the $n$-point correlation functions of the XXZ Heisenberg
spin-$1 \over 2$ chain in a constant magnetic field. For zero magnetic field,
this result agrees, in both the massless and massive (anti-ferromagnetic)
regimes, with the one obtained from the q-deformed KZ equations (massless
regime) and the representation theory of the quantum affine algebra ${\cal U}_q
(\hat{sl}_2)$ together with the corner transfer matrix approach (massive
regime).
