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.