  We construct a moduli space of stable pairs over a smooth projective variety,
parametrizing morphisms from a fixed coherent sheaf to a varying sheaf of fixed
topological type, subject to a stability condition. This generalizes the notion
used by Pandharipande and Thomas, following Le Potier, where the fixed sheaf is
the structure sheaf of the variety. We then describe the relevant deformation
and obstruction theories. We also show the existence of the virtual fundamental
class in special cases.
