  We generalize the concept of divergence of finitely generated groups by
introducing the upper and lower relative divergence of a finitely generated
group with respect to a subgroup. Upper relative divergence generalizes
Gersten's notion of divergence, and lower relative divergence generalizes a
definition of Cooper-Mihalik. While the lower divergence of Cooper-Mihalik can
only be linear or exponential, relative lower divergence can be any polynomial
or exponential function. In this paper, we examine the relative divergence
(both upper and lower) of a group with respect to a normal subgroup or a cyclic
subgroup. We also explore relative divergence of $\CAT(0)$ groups and
relatively hyperbolic groups with respect to various subgroups to better
understand geometric properties of these groups.
