  We prove local and global existence from large, rough initial data for a wave
map between 1+1 dimensional Minkowski space and an analytic manifold. Included
here is global existence for large data in the scale-invariant norm $\dot
L^{1,1}$, and in the Sobolev spaces $H^s$ for $s > 3/4$. This builds on
previous work in 1+1 dimensions of Pohlmeyer, Gu, Ginibre-Velo and Shatah.
