  We study maps from a 2D world-sheet to a 2D target space which include folds.
The geometry of folds is discussed and a metric on the space of folded maps is
written down. We show that the latter is not invariant under area preserving
diffeomorphisms of the target space. The contribution to the partition function
of maps associated with a given fold configuration is computed. We derive a
description of folds in terms of Feynman diagrams. A scheme to sum up the
contributions of folds to the partition function in a special case is suggested
and is shown to be related to the Baxter-Wu lattice model. An interpretation of
folds as trajectories of particles in the adjoint representation of $SU(N)$
gauge group in the large $N$ limit which interact in an unusual way with the
gauge fields is discussed.
