  We introduce the process of symplectic reduction along a submanifold as a
uniform approach to taking quotients in symplectic geometry. This construction
holds in the categories of smooth manifolds, complex analytic spaces, and
complex algebraic varieties, and has an interpretation in terms of derived
stacks in shifted symplectic geometry. It also encompasses
Marsden--Weinstein--Meyer reduction, Mikami--Weinstein reduction, the
pre-images of Poisson transversals under moment maps, symplectic cutting,
symplectic implosion, and the Ginzburg--Kazhdan construction of
Moore--Tachikawa varieties in TQFT. A key feature of our construction is a
concrete and systematic association of a Hamiltonian $G$-space
$\mathfrak{M}_{G, S}$ to each pair $(G,S)$, where $G$ is any Lie group and
$S\subseteq\mathrm{Lie}(G)^*$ is any submanifold satisfying certain
non-degeneracy conditions. The spaces $\mathfrak{M}_{G, S}$ satisfy a universal
property for symplectic reduction which generalizes that of the universal
imploded cross-section. While these Hamiltonian $G$-spaces are explicit and
natural from a Lie-theoretic perspective, some of them appear to be new.
