By finite volume hyperbolic 3-manifold, I do mean $M=\mathbb{H}^{3}/\Gamma$ where $\Gamma$ is a torsion-free Kleinian group such that the hyperbolic volume $Vol(M)<\infty$.

I will call $$\mathcal{M}:=\{\textrm{finite volume hyperbolic 3-manifolds}\}/_{\cong_ {isometry}} $$

The moludi space of finite volume hyperbolic 3-manifolds. As far as I understand, the hyperbolic volume function $$Vol: \mathcal{M} \rightarrow \mathbb{R}^{+}$$ has some nice properties: the image of this function is closed and well-ordered subset of $\mathbb{R}^{+}$ and the preimage $Vol(x)^{-1}$ is finite for any $x\in \mathbb{R}^{+}$

I have no knowledge in this field, but out of curiosity I wanted to know if there is some research done in understanding $\mathcal{M}$, is there a natural topological structure on it? is $\mathcal{M}$ an manifold or an orbifold ? Can we endow $\mathcal{M}$ with some algebraic or geometrical structure ?