  In this paper, following Sullivan, Kusner, and Schmitt, we study conformal
immersions of Riemann surfaces into the three-dimensional Euclidean space.
Regarding such immersions as special bundle maps from the tangent bundle of the
surface to the cotangent bundle of the 2-dimensional sphere, we generalize the
classical Weierstrass representation of minimal surfaces to the case of
arbitrary conformal immersions. We study how such an immersion gives rise to a
spin structure on the surface together with a pair of spinors and how the
immersion itself can be studied by means of these spinors.
