topological group
group that is a topological space with continuous group action
Lie group
group that is also a smooth manifold with group operations that are smooth
topological vector space
vector space equipped with a compatible topology
string group
topological group, not presentable as a finite-dimensional Lie group, but presentable as a Frechet Lie group, obtained by killing the third homotopy group of the spin group
gauge group
group of gauge symmetries in a gauge theory
loop group
loop space over a Lie group