  In this article, we classify the irreducible components of moduli stacks of
torsion free sheaves of rank 2 on K3 surfaces of Picard number 1. For ruled
surfaces, the components of moduli stacks of torsion free sheaves were
classified by C.Walter. Moreover, by virtue of our result, we classify the
irreducible components of Brill-Noether loci of Hilbert schemes of points on K3
surfaces.
