  The Vlasov equation of kinetic theory is introduced and the Hamiltonian
structure of its moments is presented. Then we focus on the geodesic evolution
of the Vlasov moments. As a first step, these moment equations generalize the
Camassa-Holm equation to its multi-component version. Subsequently, adding
electrostatic forces to the geodesic moment equations relates them to the
Benney equations and to the equations for beam dynamics in particle
accelerators. Next, we develop a kinetic theory for self assembly in
nano-particles. Darcy's law is introduced as a general principle for
aggregation dynamics in friction dominated systems (at different scales). Then,
a kinetic equation is introduced for the dissipative motion of isotropic
nano-particles. The zeroth-moment dynamics of this equation recovers the
classical Darcy's law at the macroscopic level. A kinetic-theory description
for oriented nano-particles is also presented. At the macroscopic level, the
zeroth moments of this kinetic equation recover the magnetization dynamics of
the Landau-Lifshitz-Gilbert equation. The moment equations exhibit the
spontaneous emergence of singular solutions (clumpons) that finally merge in
one singularity. This behaviour represents aggregation and alignment of
oriented nano-particles. Finally, the Smoluchowski description is derived from
the dissipative Vlasov equation for anisotropic interactions. Various levels of
approximate Smoluchowski descriptions are proposed as special cases of the
general treatment. As a result, the macroscopic momentum emerges as an
additional dynamical variable that in general cannot be neglected.
