  We examine the tidal deformation of a nonrotating compact body (material body
or black hole) in general relativity. The body's exterior metric is calculated
in a simultaneous expansion in powers of the ratio between the distance to the
body and three distinct length scales: the radius of curvature of the external
spacetime in which the body is inserted, the scale of spatial inhomogeneity of
the curvature, and the scale of temporal variation. The metric is valid in the
body's immediate neighborhood, which excludes the external matter responsible
for the tidal environment. The body's tidal response is encapsulated in four
types of relativistic Love numbers: $k_\ell$, the familiar Love number that
measures the linear response to a static tidal field, $p_\ell$, which measures
the quadratic response to the tidal field, $\dot{k}_\ell$ and $\ddot{k}_\ell$,
associated with first and second time derivatives of the tidal field,
respectively. The Love numbers acquire an operational meaning through the
definition of tidally induced multipole moments. Previously proposed
definitions for the moments suffer from ambiguities associated with the
subtraction of a "pure tidal field" from the full metric. A robust operational
definition is proposed here. It relies on inserting the body's local metric
within a global metric constructed in post-Newtonian theory; the global metric
includes the external matter responsible for the tidal environment. When viewed
in the post-Newtonian spacetime, the compact body appears as a skeletonized
object with a specific multipole structure. The tidally induced multipole
moments provide a description of this structure. They manifest themselves, for
example, in the body's tidal acceleration, which is nonlinear in the tidal
field. At leading order in the tidal interaction, the acceleration is
proportional to the $k_2$ Love number as calculated in full general relativity.
