  We construct the external metric of a slowly rotating, tidally deformed
material body in general relativity. The tidal forces acting on the body are
assumed to be weak and to vary slowly with time, and the metric is obtained as
a perturbation of a background metric that describes the external geometry of
an isolated, slowly rotating body. The tidal environment is generic and
characterized by two symmetric-tracefree tidal moments E_{ab} and B_{ab}, and
the body is characterized by its mass M, its radius R, and a dimensionless
angular-momentum vector \chi^a << 1. The perturbation accounts for all
couplings between \chi^a and the tidal moments. The body's gravitational
response to the applied tidal field is measured in part by the familiar
gravitational Love numbers K^{el}_2 and K^{mag}_2, but we find that the
coupling between the body's rotation and the tidal environment requires the
introduction of four new quantities, which we designate as rotational-tidal
Love numbers. All these Love numbers are gauge invariant in the usual sense of
perturbation theory, and all vanish when the body is a black hole.
