The Vlasov-Poisson Equation describes the dynamics of particles affected
only by non-relativistic gravity in vacuum. We will revisit work by Ye,
Morrison, and Crawford from 1991 about the space of densities as a
Poisson manifold, decomposition of solutions, and finally an alternate
equation, that restricts the set of accessible densities in a reasonable
manner. In all these topics, we will present recent rigorous work on
results that still lacked proofs.