  We study relativized Lascar groups, which are formed by relativizing Lascar
groups to the solution set of a partial type $\Sigma$. We introduce the notion
of a Lascar tuple for $\Sigma$ and by considering the space of types over a
Lascar tuple for $\Sigma$, the topology for a relativized Lascar group is
(re-)defined and some fundamental facts about the Galois groups of first-order
theories are generalized to the relativized context. In particular, we prove
that any closed subgroup of a relativized Lascar group corresponds to a
stabilizer of a bounded hyperimaginary having at least one representative in
the solution set of the given partial type $\Sigma$. Using this, we find the
correspondence between subgroups of the relativized Lascar group and the
relativized strong types. We also compare the relativized notion with the
restricted one, and provide a condition when two notions coincide.
