Einstein-Vlasov system is a coupled systems of partial differential
equations
describing the time-evolution of a galaxy or a galaxy cluster. 
It is the relativistic analog of its Newtonian counterpart: the
gravitational Vlasov-Poisson system.  
We will focus on the problem of stability of steady state galaxies, in
particular providing an overview of known results and methods in the
Newtonian case. We will then present a rigorous linearized stability
result
for the spherically symmetric Einstein-Vlasov system and a new coercivity
bound, that should present an essential step for the fully non-linear
stability. This is joint work with Gerhard Rein (University of Bayreuth,
Germany).