  For a Gorenstein curve X and a nonsingular point P of X, we construct Abel
maps A from X to J_X^1 and A_P from X to J_X^0, where J_X^i is the moduli
scheme for simple, torsion-free, rank-1 sheaves on X of degree i. The image
curves of A and A_P are shown to have the same arithmetic genus of X. Also, A
and A_P are shown to be embeddings away from rational subcurves L of X meeting
the closure of X-L in separating nodes. Finally, we establish a connection with
Seshadri's moduli scheme U_X(1) for semistable, torsion-free, rank-1 sheaves on
X, obtaining an embedding of A(X) into U_X(1).
