  In his 1957 paper, John Milnor introduced a collection of invariants for
links in $S^3$ detecting higher-order linking phenomena by studying lower
central quotients of link groups and comparing them to those of the unlink.
These invariants, now known as Milnor's $\overline{\mu}$-invariants, were later
shown to be topological link concordance invariants and have since inspired
decades of consequential research. Milnor's invariants have many
interpretations, and there have been numerous attempts to extend them to other
settings. In this paper, we extend Milnor's invariants to topological
concordance invariants of knots and links in general closed orientable
3-manifolds. These invariants unify and generalize all previous versions of
Milnor's invariants in dimension 3, including Milnor's original invariants for
links in $S^3$.
